Search results for "Tensor product"
showing 10 items of 58 documents
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.
Weakly uniformly continuous holomorphic functions and the approximation property
2001
Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.
Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions
2002
Our main result shows that every Montel Kothe echelon or coechelon space E of order 1 < p ≤ ∞ is nuclear if and only if for every (some) m ≥ 2 the space ((mE), τ0) of m-homegeneus polynomials on E endowed with the compact-open topology τ0 has an unconditional basis if and only if the space (ℋ(E), τδ) of holomorphic functions on E endowed with the bornological topology τδ associated to τ0 has an unconditional basis (for coechelon spaces τδ equals τ0). The main idea is to extend the concept of the Gordon-Lewis property from Banach to Frechet and (DF) spaces. In this way we obtain techniques which are used to characterize the existence of unconditional basis in spaces of m-th (symmetric) tenso…
On operator valued sequences of multipliers and R-boundedness
2007
AbstractIn recent papers (cf. [J.L. Arregui, O. Blasco, (p,q)-Summing sequences, J. Math. Anal. Appl. 274 (2002) 812–827; J.L. Arregui, O. Blasco, (p,q)-Summing sequences of operators, Quaest. Math. 26 (2003) 441–452; S. Aywa, J.H. Fourie, On summing multipliers and applications, J. Math. Anal. Appl. 253 (2001) 166–186; J.H. Fourie, I. Röntgen, Banach space sequences and projective tensor products, J. Math. Anal. Appl. 277 (2) (2003) 629–644]) the concept of (p,q)-summing multiplier was considered in both general and special context. It has been shown that some geometric properties of Banach spaces and some classical theorems can be described using spaces of (p,q)-summing multipliers. The p…
Convolution of three functions by means of bilinear maps and applications
1999
When dealing with spaces of vector-valued analytic functions there is a natural way to understand multipliers between them. If X and Y are Banach spaces and L(X,Y ) stands for the space of linear and continuous operators we may consider the convolution of L(X,Y )-valued analytic functions, say F (z) = ∑ n=0∞ Tnz , and X-valued polynomials, say f(z) = ∑m n=0 xnz , to get the Y -valued function F ∗ f(z) = ∑ Tn(xn)z. The second author considered such a definition and studied multipliers between H(X) and BMOA(Y ) in [5]. When the functions take values in a Banach algebra A then the natural extension of multiplier is simply that if f(z) = ∑ anz n and g(z) = ∑ bnz , then f ∗ g(z) = ∑ an.bnz n whe…
ON TOPOLOGICAL SPACES WITH A UNIQUE QUASI-PROXIMITY
1994
Abstract Trying to solve the question of whether every T 1 topological space with a unique compatible quasi-proximity should be hereditarily compact, we show that it is true for product spaces as well as for locally hereditarily Lindelof spaces.
On irreducible products of characters
2021
Abstract We study the problem when the product of two non-linear Galois conjugate characters of a finite group is irreducible. We also prove new results on irreducible tensor products of cross-characteristic Brauer characters of quasisimple groups of Lie type.
Differential algebras in non-commutative geometry
1993
We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra. For that we derive a general formula for differential algebras based on tensor products of algebras. The result is used to characterize differential algebras which appear in models with one symmetry breaking scale.
Gravity, Non-Commutative Geometry and the Wodzicki Residue
1993
We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat kernel expansion of $D^{2}$. We use this result to derive a gravity action for commutative geometry which is the usual Einstein Hilbert action and we also apply our results to a non-commutative extension which, is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological co…