Статьи журнала - Владикавказский математический журнал
Все статьи: 995
On a question on Banach - Stone theorem
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We present a very simple and elementary proof of the main theorem of [l]. This also gives an answer to a conjecture in [1].
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On b-weakly demicompact operators on Banach lattices
Статья научная
Aqzzouz and Elbour proved that an operator T on a Banach lattice E is b-weakly compact if and only if ∥Txn∥→0 as n→∞ for each b-order bounded weakly sequence {xn} in E+. In this present paper, we introduce and study new concept of operators that we call b-weakly demicompact, use it to generalize known classes of operators which defined by b-weakly compact operators. An operator T on a Banach lattice E is said to be b-weakly demicompact if for every b-order bounded sequence {xn} in E+ such that xn→0 in σ(E,E′) and ∥xn-Txn∥→0 as n→∞, we have ∥xn∥→0 as n→∞. As consequence, we obtain a characterization of KB-spaces in terms of b-weakly demicompact operators. After that, we investigate the relationships between b-weakly demicompact operators and some other classes of operators on Banach lattices espaciallly their relationships with demi Dunford-Pettis operators and order weakly demicompact operators.
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On collectively-Levi sets of operators
Статья научная
The Levi operators are operator abstractions of the Levy property of Banach lattices. Such operators have been studied recently by several authors. The present paper deals with the collective properties of the Levi operators of several kinds: σ-Levi operators; quasi c-σ-Levi operators; and quasi σ-Levi operators. A notion of collectively σ-Levi set generalizes the notion of a single σ-Levi operator to the families of operators. Working with families of sequences of elements of a vector lattice requires the notion of the collective order convergence. This notion that is introduced and studied in the present paper may have its own interest and further possible applications. Various relations of the collectively quasi σ-Levi sets to the collectively compact sets are investigated. The domination problem for the collectively quasi σ-Levi sets is studied. In this study a special notion of a set of operators dominated by another set of operators is used.
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On combined nonstandard methods in functional analysis
Статья научная
The main nonstandard tool-kits are known as infinitesimal analysis (Robinson's nonstandard analysis) and Boolean-valued analysis. Sharp distinctions between these two versions of nonstandard analysis in content and technique notwithstanding, many ways are open to their simultaneous application. One of the simplest approaches consists in successive application of different nonstandard methods. It is demonstrated that combining is often useful in settling the problems of functional analysis which stem mainly from the theory of vector lattices.
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On conservation laws in affine toda systems
Статья научная
With the help of certain matrix decomposition and projectors of special forms we show that non-Abelian Toda systems associated with loop groups possess infinite sets of conserved quantities following from essentially different conservation laws.
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On extreme extension of positive operators
Статья научная
Given vector lattices E, F and a positive operator S from a majorzing subspace D of E to F, denote by E(S) the collection of all positive extensions of S to all of E. This note aims to describe the collection of extreme points of the convex set E(T∘S). It is proved, in particular, that E(T∘S) and T∘E(S) coincide and every extreme point of E(T∘S) is an extreme point of T∘E(S), whenever T:F→G is a Maharam operator between Dedekind complete vector lattices. The proofs of the main results are based on the three ingredients: a characterization of extreme points of subdifferentials, abstract disintegration in Kantorovich spaces, and an intrinsic characterization of subdifferentials.
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On finite homogeneous metric spaces
Статья научная
This survey is devoted to recently obtained results on finite homogeneous metric spaces. The main subject of discussion is the classification of regular and semiregular polytopes in Euclidean spaces by whether or not their vertex sets have the normal homogeneity property or the Clifford - Wolf homogeneity property. Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces. The normal generalized homogeneity and the Clifford - Wolf homogeneity describe more stronger properties than the homogeneity. Therefore, it is natural to first check the presence of these properties for the vertex sets of regular and semiregular polytopes. In addition to the classification results, the paper contains a description of the main tools for the study of the relevant objects.
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On generalization of Fourier and Hartley transforms for some quotient class of sequences
Статья научная
In this paper we consider a class of distributions and generate two spaces of Boehmians for certain class of integral operators. We derive a convolution theorem and generate two spaces of Boehmians. The integral operator under concern is well-defined, linear and one-to-one in the class of Boehmians. An inverse problem is also discussed in some details.
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On generalized Kenmotsu manifolds as hypersurfaces of Vaisman-Gray manifolds
Статья научная
In this paper, we conclude that the hypersurfaces of Vaisman-Gray manifolds have generalized Kenmotsu structures under some conditions for the Lee form, Kirichenko's tensors and the second fundamental form of the immersion of the hypersurface into the manifold of Vaisman-Gray class. Moreover, the components of the second fundamental form are determined when the foregoing hypersurfaces have generalized Kenmotsu structures or any special kind of it or Kenmotsu structures, such that some of these components are vanish. Also, some components of Lee form and some components of some Kirichenko's tensors in the Vaisman-Gray class are equal to zero. On the other hand, the minimality of totally umbilical, totally geodesic hypersurfaces of Vaisman-Gray manifolds with generalized Kenmotsu structures are investigated. In addition, we deduced that the hypersurface of Vaisman-Gray manifold that have generalized Kenmotsu structure is totally geodesic if and only if it is totally umbilical and some components of Lee form are constants.
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On ideal of compact operators in real factors
Статья научная
In the present paper the real ideals of relatively compact operators of W*-algebras are considered. A description (up to isomorphism) of real two-sided ideal of relatively compact operators of the complex W*-factors is given.
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On meromorphic function with maximal deficiency sum and it's difference operators
Статья научная
The paper deals with characteristic funtion and deficiency of a meromorphic function. We mainly focused on the relation between the characteristic function of a product of difference operators with the characteristic function of a meromorphic function with maximal deficiency sum. The concept of maximal deficiency sum of a meromorphic function is employed as an effective tool for our research. In the same context, the notion of a difference polynomial of a difference operator is discussed. The paper contains the details analysis and discussion of some asymptotic behaviour of the product of difference operators, such as limr→∞T(r,∏qi=1Δηif)T(r,f), limr→∞N(r,0;∏qi=1Δηif)T(r,∏qi=1Δηif), lim r→∞N(r,∞;∏qi=1Δηif)+N(r,0;∏qi=1Δηif)T(r,∏qi=1Δηif) etc. and same resolution and discussion also developed for the difference polynomial of difference operators. Several innovative idea to establish some inequalities on the zeros and poles for ∏qi=1Δηif and L(Δηf) are also introduced. We broadly elaborate our results with many remarks and corollaries, and give two excellent examples for proper justification of our results. The results on product and polynomial of difference operators of our article improved and generalised the results of Z. Wu.
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On minimax theorems for sets closed in measure
Статья научная
This article is devoted to the Ky Fan minimax theorem for convex sets closed in measure in L^1. In general, these sets do not carry any formal compactness properties for any reasonable topology.
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On neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras
Статья научная
Some ergodic type theorems for automorphisms of semi-finite von Neumann algebras are considered. Neveu decomposition is employed in order to prove stochastical convergence. This work is a generalization of authors results from [5] to the case of semi-finite von Neumann algebras.
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On non-commutative ergodic type theorems for free finitely generated semigroups
Статья научная
In the paper the authors generalize Bufetov's Ergodic Type Theorems to the case of the actions of free finitely generated semigroups on von Neumann algebras.
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On normal subgroups of the group representation of the Cayley tree
Статья научная
Gibbs measure plays an important role in statistical mechanics. On a Cayley tree, for describing periodic Gibbs measures for models in statistical mechanics we need subgroups of the group representation of the Cayley tree. A normal subgroup of the group representation of the Cayley tree keeps the invariance property which is a significant tool in finding Gibbs measures. By this occasion, a full description of normal subgroups of the group representation of the Cayley tree is a significant problem in Gibbs measure theory. For instance, in [1, 2] a full description of normal subgroups of indices four, six, eight, and ten for the group representation of a Cayley tree is given. The present paper is a generalization of these papers, i. e., in this paper, for any odd prime number p, we give a characterization of the normal subgroups of indices 2n, n∈{p,2p} and 2i,i∈N, of the group representation of the Cayley tree.
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On positive invertibility and splittings of operators in ordered Banach spaces
Статья научная
The positive invertibility of operators between Banach spaces, ordered by special closed cones, is characterized by the existence of splittings for the operators into the difference of two operators with appropriate spectral properties. Some results, up to now known only for matrices, are generalized to operators and to order intervals of operators.
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On projective limits of real C*-algebras and Jordan operator algebras
Статья научная
In the present paper a real and Jordan analogues of complex locally C*-algebras are introduced. Their definitions and basic properties are discussed.
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On some properties of extensions of commutative unital rings
Статья научная
We find necessary and sufficient conditions for the ring R[α] to be either a field or a domain whenever R is a commutative ring with 1 and α is an algebraic element over R. This continues the studies started by Nachev (Compt. Rend. Acad. Bulg. Sci., 2004) and (Commun. Alg., 2005) as well as their generalization due to Mihovski (Compt. Rend. Acad. Bulg. Sci., 2005).
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On some properties of orthosymmetric bilinear operators
Статья научная
This note contains some properties of positive orthosymmetric bilinear operators on vector lattices which are well known for almost f-algebra multiplication but despite of their simplicity does not seem appeared in the literature.
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On stability of retro Banach frame with respect to b-linear functional in n-Banach space
Статья научная
We introduce the notion of a retro Banach frame relative to a bounded b-linear functional in n-Banach space and see that the sum of two retro Banach frames in n-Banach space with different reconstructions operators is also a retro Banach frame in n-Banach space. Also, we define retro Banach Bessel sequence with respect to a bounded b-linear functional in n-Banach space. A necessary and sufficient condition for the stability of retro Banach frame with respect to bounded b-linear functional in n-Banach space is being obtained. Further, we prove that retro Banach frame with respect to bounded b-linear functional in n-Banach space is stable under perturbation of frame elements by positively confined sequence of scalars. In n-Banach space, some perturbation results of retro Banach frame with the help of bounded b-linear functional in n-Banach space have been studied. Finally, we give a sufficient condition for finite sum of retro Banach frames to be a retro Banach frame in n-Banach space. At the end, we discuss retro Banach frame with respect to a bounded b-linear functional in Cartesian product of two n-Banach spaces.
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