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Higher-dimensional weak amenability

B. Johnson — 1997

Studia Mathematica

Bade, Curtis and Dales have introduced the idea of weak amenability. A commutative Banach algebra A is weakly amenable if there are no non-zero continuous derivations from A to A*. We extend this by defining an alternating n-derivation to be an alternating n-linear map from A to A* which is a derivation in each of its variables. Then we say that A is n-dimensionally weakly amenable if there are no non-zero continuous alternating n-derivations on A. Alternating n-derivations are the same as alternating...

Some examples in harmonic analysis

B. Johnson — 1973

Studia Mathematica

Operators into $L_{p}$ which factor through $l_{p}$

W. B. Johnson

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Banach spaces all of whose subspaces have the approximation property

W. B. Johnson

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Complemented subspaces of $L_{p}$ which embed into $ℓ_{p} \otimes ℓ_{2}$

W. B. Johnson

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

A universal non-compact operator

William B. Johnson — 1971

Colloquium Mathematicae

On quotients of $L_{p}$ which are quotients of $ℓ_{p}$

W. B. Johnson — 1977

Compositio Mathematica

$ϰ$ -Lindelöf locales and their spatial parts

P. B. Johnson — 1991

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Coherent spaces constructively

P. B. Johnson — 1996

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Finite-dimensional Schauder decompositions in certain Frechet spaces

William B. Johnson — 1971

Colloquium Mathematicae

A classification of degree $n$ functors, II

B. Johnson; R. McCarthy — 2003

Cahiers de Topologie et Géométrie Différentielle Catégoriques

A classification of degree $n$ functors, I

B. Johnson; R. McCarthy — 2003

Cahiers de Topologie et Géométrie Différentielle Catégoriques

A uniformly convex Banach space which contains no $l_{p}$

T. Figiel; W. B. Johnson — 1974

Compositio Mathematica

Subspaces of $L_{p}$ which embed into $l_{p}$

W. B. Johnson; E. Odell — 1974

Compositio Mathematica

The dual form of the approximation property for a Banach space and a subspace

T. Figiel; W. B. Johnson — 2015

Studia Mathematica

Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. In particular, if the pair (X,Y) has the AP then X, Y, and the quotient space X/Y have the classical Grothendieck AP. The main result is an easy to apply dual formulation of this property. Applications...

Stability of Banach algebras

Johnson, B. E. — 1977

General topology and its relations to modern analysis and algebra IV

Stochastic approximation properties in Banach spaces

V. P. Fonf; W. B. Johnson; G. Pisier; D. Preiss — 2003

Studia Mathematica

We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an $L_{p}$ space into X whose range has probability one, then X is a quotient of an $L_{p}$ space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for...

Corrigendum to “Commutators on ${(\sum ℓ_{q})}_{p}$ ” (Studia Math. 206 (2011), 175-190)

Dongyang Chen; William B. Johnson; Bentuo Zheng — 2014

Studia Mathematica

We give a corrected proof of Theorem 2.10 in our paper “Commutators on ${(\sum ℓ_{q})}_{p}$ ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.

Commutators on ${(\sum ℓ_{q})}_{p}$

Dongyang Chen; William B. Johnson; Bentuo Zheng — 2011

Studia Mathematica

Let T be a bounded linear operator on $X = {(\sum ℓ_{q})}_{p}$ with 1 ≤ q < ∞ and 1 < p < ∞. Then T is a commutator if and only if for all non-zero λ ∈ ℂ, the operator T - λI is not X-strictly singular.

Linear contraction mappings

Johnson, William B.; Shive, Robert A. jr. — 1971

Portugaliae mathematica

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Currently displaying 1 – 20 of 20

Higher-dimensional weak amenability

Some examples in harmonic analysis

Operators into $L_{p}$ which factor through $l_{p}$

Banach spaces all of whose subspaces have the approximation property

Complemented subspaces of $L_{p}$ which embed into $ℓ_{p} \otimes ℓ_{2}$

A universal non-compact operator

On quotients of $L_{p}$ which are quotients of $ℓ_{p}$

$ϰ$ -Lindelöf locales and their spatial parts

Coherent spaces constructively

Finite-dimensional Schauder decompositions in certain Frechet spaces

A classification of degree $n$ functors, II

A classification of degree $n$ functors, I

A uniformly convex Banach space which contains no $l_{p}$

Subspaces of $L_{p}$ which embed into $l_{p}$

The dual form of the approximation property for a Banach space and a subspace

Stability of Banach algebras

Stochastic approximation properties in Banach spaces

Corrigendum to “Commutators on ${(\sum ℓ_{q})}_{p}$ ” (Studia Math. 206 (2011), 175-190)

Commutators on ${(\sum ℓ_{q})}_{p}$

Linear contraction mappings