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Diameter, extreme points and topology

J. C. Navarro-Pascual, M. G. Sanchez-Lirola (2009)

Studia Mathematica

We study the extremal structure of Banach spaces of continuous functions with the diameter norm.

Disjoint hypercyclic powers of weighted translations on groups

Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou (2017)

Czechoslovak Mathematical Journal

Let G be a locally compact group and let 1 p < . Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space L p ( G ) in terms of the weights. Sufficient and...

Dual Spaces and Hahn-Banach Theorem

Keiko Narita, Noboru Endou, Yasunari Shidama (2014)

Formalized Mathematics

In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved the Hahn-Banach...

Duality on vector-valued weighted harmonic Bergman spaces

Salvador Pérez-Esteva (1996)

Studia Mathematica

We study the duals of the spaces A p α ( X ) of harmonic functions in the unit ball of n with values in a Banach space X, belonging to the Bochner L p space with weight ( 1 - | x | ) α , denoted by L p α ( X ) . For 0 < α < p-1 we construct continuous projections onto A p α ( X ) providing a decomposition L p α ( X ) = A p α ( X ) + M p α ( X ) . We discuss the conditions on p, α and X for which A p α ( X ) * = A q α ( X * ) and M p α ( X ) * = M q α ( X * ) , 1/p+1/q = 1. The last equality is equivalent to the Radon-Nikodým property of X*.

Duality theory of spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Let X be a completely regular Hausdorff space, E a real normed space, and let C b ( X , E ) be the space of all bounded continuous E -valued functions on X . We develop the general duality theory of the space C b ( X , E ) endowed with locally solid topologies; in particular with the strict topologies β z ( X , E ) for z = σ , τ , t . As an application, we consider criteria for relative weak-star compactness in the spaces of vector measures M z ( X , E ' ) for z = σ , τ , t . It is shown that if a subset H of M z ( X , E ' ) is relatively σ ( M z ( X , E ' ) , C b ( X , E ) ) -compact, then the set conv ( S ( H ) ) is still relatively σ ( M z ( X , E ' ) , C b ( X , E ) ) -compact...

Dynamics of differentiation and integration operators on weighted spaces of entire functions

María J. Beltrán (2014)

Studia Mathematica

We investigate the dynamical behavior of the operators of differentiation and integration and the Hardy operator on weighted Banach spaces of entire functions defined by integral norms. In particular we analyze when they are hypercyclic, chaotic, power bounded, and (uniformly) mean ergodic. Moreover, we estimate the norms of the operators and study their spectra. Special emphasis is put on exponential weights.

Dynamics of differentiation operators on generalized weighted Bergman spaces

Liang Zhang, Ze-Hua Zhou (2015)

Open Mathematics

The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.

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