Search results for "paces"

Banach partial *-algebras: an overview

2019

A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely, $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.

Tensor products of Fréchet or (DF)-spaces with a Banach space

1992

Abstract The aim of the present article is to study the projective tensor product of a Frechet space and a Banach space and the injective tensor product of a (DF)-space and a Banach space. The main purpose is to analyze the connection of the good behaviour of the bounded subsets of the projective tensor product and of the locally convex structure of the injective tensor product with the local structure of the Banach space.

Rigged Hilbert spaces and contractive families of Hilbert spaces

2013

The existence of a rigged Hilbert space whose extreme spaces are, respectively, the projective and the inductive limit of a directed contractive family of Hilbert spaces is investigated. It is proved that, when it exists, this rigged Hilbert space is the same as the canonical rigged Hilbert space associated to a family of closable operators in the central Hilbert space.

Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

2015

Abstract This paper deals with the eigenvalue problem for the operator L = − Δ − x ⋅ ∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λ k of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c > 0 and k ∈ N the following minimization problem min ⁡ { λ k ( Ω ) : Ω quasi-open set , ∫ Ω e | x | 2 / 2 d x ≤ c } has a solution.

On the irreducibility of Hurwitz spaces of coverings with two special fibers

2012

Some Inclusion Theorems for Orlicz and Musielak-Orlicz Type Spaces

1995

where K is a homogeneous kernel and f belongs to some KSthe functional space. In these papers the estimates are taken with respect to the KSthe norm of the space. Recently in [2] we obtained analogous estimates for functions belonging to Orlicz or Musielak-Orlicz type spaces L ~, with respect to the canonical modular functional. These results enable us to say that, for example,

On the notion of parallel transport on RCD spaces

2019

We propose a general notion of parallel transport on RCD spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space. peerReviewed

Ulam Stability for the Composition of Operators

2020

Working in the setting of Banach spaces, we give a simpler proof of a result concerning the Ulam stability of the composition of operators. Several applications are provided. Then, we give an example of a discrete semigroup with Ulam unstable members and an example of Ulam stable operators on a Banach space, such that their sum is not Ulam stable. Another example is concerned with a C 0 -semigroup ( T t ) t &ge

Hardy-Orlicz Spaces of conformal densities

2014

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.

Frames and representing systems in Fréchet spaces and their duals

2014

[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.