Search results for " Tensor"
showing 10 items of 210 documents
Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions
2017
Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.
Injective spaces of real-valued functions with the baire property
1995
Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.
Factorization of (q,p)-summing polynomials through Lorentz spaces
2017
[EN] We present a vector valued duality between factorable (q,p)-summing polynomials and (q,p)-summing linear operators on symmetric tensor products of Banach spaces. Several applications are provided. First, we prove a polynomial characterization of cotype of Banach spaces. We also give a variant of Pisier's factorization through Lorentz spaces of factorable (q,p)-summing polynomials from C(K)-spaces. Finally, we show a coincidence result for (q,p)-concave polynomials.(c) 2016 Elsevier Inc. All rights reserved.
Property (M) and the weak fixed point property
1997
It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.
Unconditional Basis and Gordon–Lewis Constants for Spaces of Polynomials
2001
Abstract No infinite dimensional Banach space X is known which has the property that for m ⩾2 the Banach space of all continuous m -homogeneous polynomials on X has an unconditional basis. Following a program originally initiated by Gordon and Lewis we study unconditionality in spaces of m -homogeneous polynomials and symmetric tensor products of order m in Banach spaces. We show that for each Banach space X which has a dual with an unconditional basis ( x * i ), the approximable (nuclear) m -homogeneous polynomials on X have an unconditional basis if and only if the monomial basis with respect to ( x * i ) is unconditional. Moreover, we determine an asymptotically correct estimate for the …
Some Classes of Operators on Partial Inner Product Spaces
2012
Many families of function spaces, such as $L^{p}$ spaces, Besov spaces, amalgam spaces or modulation spaces, exhibit the common feature of being indexed by one parameter (or more) which measures the behavior (regularity, decay properties) of particular functions. All these families of spaces are, or contain, scales or lattices of Banach spaces and constitute special cases of the so-called \emph{partial inner product spaces (\pip s)} that play a central role in analysis, in mathematical physics and in signal processing (e.g. wavelet or Gabor analysis). The basic idea for this structure is that such families should be taken as a whole and operators, bases, frames on them should be defined glo…
Pietsch's factorization theorem for dominated polynomials
2007
Abstract We prove that, like in the linear case, there is a canonical prototype of a p -dominated homogeneous polynomial through which every p -dominated polynomial between Banach spaces factors.
Preduals of spaces of homogeneous polynomials onLp-spaces
2012
Given a regular probability measure μ on a compact Hausdorff space, we explicitly describe the predual of the Banach space of continuous n-homogeneous polynomials on L p (μ) as the completion of a (explicit constructed) subspace of L p/n (μ) with respect to a (explicitly constructed) norm π p/n . An application to the factorization of dominated polynomials is provided.
Automatic continuity of generalized local linear operators
1980
In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.
On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials
2007
Given an operator ideal I, we study the multi-ideal I ο L and the polynomial ideal I ο P). The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained.