Wyniki wyszukiwania

1

M-complete approximate identities in operator spaces

100%

Arias A., Rosenthal H. P.

Studia Mathematica

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2000

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tom 141

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nr 2

143-200

EN

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai's generalize central approximate identities in ideals in C*-algebras, for it is proved that if X admits an M-cai in Y, then X is a complete M-ideal in Y. It is proved, using 'special' M-cai's, that if J is a nuclear ideal in a C*-algebra A, then J is completely complemented in Y for any (isomorphically) locally reflexive operator space Y with J ⊂ Y ⊂ A and Y/J separable. (This generalizes the previously known special case where Y=A , due to Effros-Haagerup.) In turn, this yields a new proof of the Oikhberg-Rosenthal Theorem that K is completely complemented in any separable locally reflexive operator superspace, where K is the C*-algebra of compact operators on $l^2$. M-cai's are also used in obtaining some special affirmative answers to the open problem of whether K is Banach-complemented in A for any separable C*-algebra A with $K ⊂A ⊂ B(l^2)$. It is shown that if, conversely, X is a complete M-ideal in Y, then X admits an M-cai in Y in the following situations: (i) Y has the (Banach) bounded approximation property; (ii) Y is 1-locally reflexive and X is λ-nuclear for some λ ≥ 1; (iii) X is a closed 2-sided ideal in an operator algebra Y (via the Effros-Ruan result that then X has a contractive algebraic approximate identity). However, it is shown that there exists a separable Banach space X which is an M-ideal in Y=X**, yet X admits no M-approximate identity in Y.

2

On ω*-basic sequences and their applications to the study of Banach spaces

80%

Johnson W. B., Rosenthal H. P.

Studia Mathematica

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1972

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tom 43

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nr 1

77-92

3

On Banach spaces X for which $Π_{2}(ℒ_{∞},X)=B(ℒ_{∞},X)$

70%

Dubinsky E., Pełczyński A., Rosenthal H. P.

Studia Mathematica

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1972

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tom 44

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nr 6

617-648

4

Localization techniques in $L^{p}$ spaces

50%

Pełczyński A., Rosenthal H. P.

Studia Mathematica

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1974-1975

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tom 52

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nr 3

265-289

5

Normalized weakly null sequence with no unconditional subsequence

41%

Maurey B., Rosenthal H. P.

Studia Mathematica

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1977

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tom 61

|

nr 1

77-98

Ograniczanie wyników

5 Studia Mathematica

5 Rosenthal H. P.

2 Pełczyński A.

1 Arias A.

1 Dubinsky E.

1 Johnson W. B.

1 Maurey B.

1 2000

1 1977

1 1975

2 1972

M-complete approximate identities in operator spaces

On ω*-basic sequences and their applications to the study of Banach spaces

On Banach spaces X for which $Π_{2}(ℒ_{∞},X)=B(ℒ_{∞},X)$

Localization techniques in $L^{p}$ spaces

Normalized weakly null sequence with no unconditional subsequence