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On the structure of tensor norms related to (p,σ)-absolutely continuous operators.

Enrique A. Sánchez-Pérez (1996)

Collectanea Mathematica

We define an interpolation norm on tensor products of p-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of (p, sigma)-absolutely continuous operators defined by Jarchow and Matter. As...

On the vector-valued Fourier transform and compatibility of operators

In Sook Park (2005)

Studia Mathematica

Let be a locally compact abelian group and let 1 < p ≤ 2. ’ is the dual group of , and p’ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform F if F ⊗ T : L p ( ) ⊗ X → L p ' ( ' ) ⊗ Y admits a continuous extension [ F , T ] : [ L p ( ) , X ] → [ L p ' ( ' ) , Y ] . Let ℱ T p denote the collection of such T’s. We show that ℱ T p ℝ × = ℱ T p ℤ × = ℱ T p ℤ ⁿ × for any and positive integer n. Moreover, if the factor group of by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then ℱ T p = ℱ T p ℤ .

On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

Open partial isometries and positivity in operator spaces

David P. Blecher, Matthew Neal (2007)

Studia Mathematica

We first study positivity in C*-modules using tripotents ( = partial isometries) which are what we call open. This is then used to study ordered operator spaces via an "ordered noncommutative Shilov boundary" which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the arrows completely positive. Because of their independent interest, we also systematically study open tripotents and their properties.

Open projections in operator algebras I: Comparison theory

David P. Blecher, Matthew Neal (2012)

Studia Mathematica

We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rørdam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals...

Open projections in operator algebras II: Compact projections

David P. Blecher, Matthew Neal (2012)

Studia Mathematica

We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of 'peak projections', and in the separable case compact projections are just the peak projections. We also establish new forms of the noncommutative Urysohn lemma relative to an operator algebra, and we show that a projection is compact iff the associated face in the state space of the algebra is...

Operator algebras

T. K. Carne (1979/1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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