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Fully absolutely summing and Hilbert-Schmidt multilinear mappings.

Mário C. Matos (2003)

Collectanea Mathematica

The space of the fully absolutely (r;r1,...,rn)-summing n-linear mappings between Banach spaces is introduced along with a natural (quasi-)norm on it. If r,rk C [1,+infinite], k=1,...,n, this space is characterized as the topological dual of a space of virtually nuclear mappings. Other examples and properties are considered and a relationship with a topological tensor product is stablished. For Hilbert spaces and r = r1 = ... = rn C [2,+infinite[ this space is isomorphic to the space of the Hilbert-Schmidt...

Fully representable and *-semisimple topological partial *-algebras

J.-P. Antoine, G. Bellomonte, C. Trapani (2012)

Studia Mathematica

We continue our study of topological partial *-algebras, focusing our attention on *-semisimple partial *-algebras, that is, those that possess a multiplication core and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals, and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the aim of characterizing a *-semisimple partial...

Fully summing mappings between Banach spaces

Mário C. Matos, Daniel M. Pellegrino (2007)

Studia Mathematica

We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.

Funciones unimodulares y acotación uniforme.

J. Fernández, S. Hui, Harold S. Shapiro (1989)

Publicacions Matemàtiques

In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H∞ with the weak-star topology.

Function algebras of Besov and Triebel-Lizorkin-type

Fares Bensaid, Madani Moussai (2023)

Czechoslovak Mathematical Journal

We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.

Function spaces have essential sets

Jan Čerych (1998)

Commentationes Mathematicae Universitatis Carolinae

It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.

Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.

Hans Triebel (2002)

Revista Matemática Complutense

Function spaces of type Bspq and Fspq cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Hölder-Zygmund spaces and inhomogeneous Hardy spaces. In the last 2 or 3 decades they haven been studied preferably on Rn and in smooth bounded domains in Rn including numerous applications to pseudodifferential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in recent times there is a...

Function spaces in the Stegall class

Ivaylo S. Kortezov (1999)

Commentationes Mathematicae Universitatis Carolinae

We prove several stability properties for the class of compact Hausdorff spaces T such that C ( T ) with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.

Function spaces of Nikolskii type on compact manifold

Cristiana Bondioli (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Nikolskii spaces were defined by way of translations on R n and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in R n , we get an equivalent definition if we replace translations by all isometries of R n . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...

Function spaces on the snowflake

Maryia Kabanava (2011)

Banach Center Publications

We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.

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