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Compact operators relative to a von Neumann algebra. (English. Russian original) Zbl 0256.47029

Funct. Anal. Appl. 6, 31-34 (1972); translation from Funkts. Anal. Prilozh. 6, No. 1, 37-40 (1972).

MSC:

47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47C15 Linear operators in \(C^*\)- or von Neumann algebras
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References:

[1] M. Breuer, ”Fredholm theories in von Neumann algebras. I,” Math. Ann.,178, 243-254 (1968). · Zbl 0162.18701
[2] I. E. Segal, ”A non-commutative extension of abstract integration,” Ann. Math.,57, 401-458 (1953). · Zbl 0051.34201
[3] V. I. Ovchinnikov, ”On the s-numbers of measurable operators,” Funktsional. Analiz i Ego Prilozhen.,4, No. 3, 78-85 (1970). · Zbl 0219.47029
[4] M. G. Konis, ”On a class of operators in von Neumann algebras with a Segal measure on the projections,” Matem. Sb.,84, 353-367 (1971).
[5] H. Umegaki, ”Conditional expectations in an operator algebra. III,” Kodai Math. Seminar Reports,11, 51-64 (1959). · Zbl 0102.10801
[6] J. Dixmier, Les Algebres d’Operateurs dans l’Espace Hilbertien, Paris (1969). · Zbl 0175.43801
[7] V. I. Ovchinnikov, Symmetric Spaces of Measurable Operators, Dokl. Akad. Nauk SSSR,191, No. 4, 769-771 (1970). · Zbl 0215.49103
[8] I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonself-adjoint Operators [in Russian], Nauka, Moscow (1965) [English translation, Amer. Math. Soc. Translations of Mathematical Monographs (1969)].
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