The uuniqueness of the symmetric structure in ideals of compact operators
Автор: Aminov Behzod Rasulovich, Chilin Vladimir Ivanovich
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 1 т.20, 2018 года.
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Let H be a separable infinite-dimensional complex Hilbert space, let L(H) be the C∗-algebra of bounded linear operators acting in H, and let K(H) be the two-sided ideal of compact linear operators in L(H). Let (E,∥⋅∥E) be a symmetric sequence space, and let CE:={x∈K(H):{sn(x)}∞n=1∈E} be the proper two-sided ideal in L(H), where {sn(x)}∞n=1 are the singular values of a compact operator x. It is known that CE is a Banach symmetric ideal with respect to the norm ∥x∥CE=∥{sn(x)}∞n=1∥E. A symmetric ideal CE is said to have a unique symmetric structure if CE=CF, that is E=F, modulo norm equivalence, whenever (CE,∥⋅∥CE) is isomorphic to another symmetric ideal (CF,∥⋅∥CF). At the Kent international conference on Banach space theory and its applications (Kent, Ohio, August 1979), A. Pelczynsky posted the following problem: (P) Does every symmetric ideal have a unique symmetric structure? This problem has positive solution for Schatten ideals Cp, 1≤p
Symmetric ideal of compact operators, uniqueness of a symmetric structure, positive isometry
Короткий адрес: https://sciup.org/143162465
IDR: 143162465 | DOI: 10.23671/VNC.2018.1.11394
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