Search results for "composition"

On compactness of the difference of composition operators

2004

Abstract Let φ and ψ be analytic self-maps of the unit disc, and denote by C φ and C ψ the induced composition operators. The compactness and weak compactness of the difference T = C φ − C ψ are studied on H p spaces of the unit disc and L p spaces of the unit circle. It is shown that the compactness of T on H p is independent of p ∈[1,∞). The compactness of T on L 1 and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H 1 but non-compact on L 1 . Other given results deal with L ∞ , weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro.

Coprime action, characters and decomposition numbers

1996

Biweights on Partial *-Algebras

2000

This chapter is devoted to the systematic investigation of biweights on partial *-algebras. These are a generalization of invariant positive sesquilinear forms that still allows a Gel’fand—Naĭmark—Segal (GNS) construction of representations. In Section 9.1, we apply this GNS construction for biweights and we obtain *-representations and cyclic vector representations of partial *-algebras, and we give some examples of biweights. Section 9.2 is devoted to the investigation of the Radon—Nikodým theorem and the Lebesgue decomposition theorem for biweights on partial *-algebras. In Section 9.3, we define regular and singular biweights on partial *-algebras and we characterize them with help of t…

Mean ergodic composition operators on Banach spaces of holomorphic functions

2016

[EN] Given a symbol cc, i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator C-phi(f) = f circle phi defined on the Banach spaces of holomorphic functions A(D) and H-infinity(D). We obtain different conditions on the symbol phi which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behavior of the iterates of the symbol. Finally, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.

Brauer characters with cyclotomic field of values

2008

It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675–686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p=2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p≠q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q(exp(2πi/q)).

The Composition Operation on Spaces of Holomorphic Mappings

2020

AbstractWe discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.

Holomorphic Hölder‐type spaces and composition operators

2020

Homological Projective Duality for Determinantal Varieties

2016

In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi-Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.

Round-handle decomposition ofS2×S1

2007

A round-handle decomposition is associated with a non-singular Morse–Smale flow on 3-manifolds prime to S 2× S 1. This decomposition has been built only for the 3-sphere S 3. In this paper we obtain the round-handle decomposition of non-singular Morse–Smale flows on S 2× S 1, in order to get all the different fattened round handles in this manifold. Some of them include non-separating boundary components that induce the topology of the links of periodic orbits.

Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

2019

The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…