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1

Interpolation by elementary operators

100%

Magajna B.

Studia Mathematica

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1993

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tom 105

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nr 1

77-92

EN

Given two n-tuples $a = (a_1,...,a_n)$ and $b = (b_1,...,b_n)$ of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that $Ea_j = b_j$ for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in $A^n$.

2

Hilbert modules and tensor products of operator spaces

100%

Magajna B.

Banach Center Publications

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1997

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tom 38

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nr 1

227-246

EN

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product $\bar{H}\hat{⨂}H$ is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C*-algebra is shown to be completely bounded with $∥ b∥_{cb}=∥ b∥ $. The so called projective operator tensor product of two operator modules X and Y over an abelian von Neumann algebra C is introduced and if Y is a Hilbert module, this product is shown to coincide with the Haagerup tensor product of X and Y over C.

3

On completely bounded bimodule maps over W*-algebras

100%

Magajna B.

Studia Mathematica

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2003

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tom 154

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nr 2

137-164

EN

It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type $I_{∞,∞}$. Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra A, is the map $q:A {⊗\limits^{eh}} X ⊗{\limits^{eh}} A → X {⊗\limits^{np}} A$, induced by q(a ⊗ x ⊗ b) = x ⊗ ab, from the extended Haagerup tensor product to the normal version of the Pisier delta tensor product a quotient map? We give a reformulation of this problem in terms of normal extension of some completely bounded maps and answer it affirmatively in the case A is of type I and X belongs to a certain class which includes all finite-dimensional operator spaces.

Ograniczanie wyników

2 Studia Mathematica

1 Banach Center Publications

3 Magajna B.

1 2003

1 1997

1 1993

Interpolation by elementary operators

Hilbert modules and tensor products of operator spaces

On completely bounded bimodule maps over W*-algebras