Factorization in Banach algebras
Factorization in Fréchet spaces
Factorization in some Fréchet algebras of differentiable functions
Factorization in the algebra of rapidly decreasing functions on
Factorization of compact operators and applications to the approximation problem
Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Factorization of Hardy Spaces on Local Fields.
Factorization of Holomorphic Mappings in Infinite Dimensions.
Factorization of mappings and general existence theorems in locally convex spaces
Factorization of Montel operators
Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.
Factorization of operators on C*-algebras
Let A be a C*-algebra. We prove that every absolutely summing operator from A into factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and with , then for every ε >0, the ε-capacity of...
Factorization of Operators Through Lp ... or Lp1 and Non-Commutative Generalizations.
Factorization of unbounded operators on Köthe spaces
The main result is that the existence of an unbounded continuous linear operator T between Köthe spaces λ(A) and λ(C) which factors through a third Köthe space λ(B) causes the existence of an unbounded continuous quasidiagonal operator from λ(A) into λ(C) factoring through λ(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (λ(A),λ(B)) ∈ ℬ (which means that all...
Factorization of uniformly holomorphic functions
Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the...
Factorization of vector measures and their integration operators
Let X be a Banach space and ν a countably additive X-valued measure defined on a σ-algebra. We discuss some generation properties of the Banach space L¹(ν) and its connection with uniform Eberlein compacta. In this way, we provide a new proof that L¹(ν) is weakly compactly generated and embeds isomorphically into a Hilbert generated Banach space. The Davis-Figiel-Johnson-Pełczyński factorization of the integration operator is also analyzed. As a result, we prove that if is both completely continuous...
Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces
Factorization of weakly continuous holomorphic mappings
We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser...
Factorization theorem for -summing operators
We study some classes of summing operators between spaces of integrable functions with respect to a vector measure in order to prove a factorization theorem for -summing operators between Banach spaces.
Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.
Factorization through Inclusion Mappings between Ip-Spaces.