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Compact widths in metric trees

Asuman Güven Aksoy, Kyle Edward Kinneberg (2011)

Banach Center Publications

The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also...

Compactness and convergence of set-valued measures

Kenny Koffi Siggini (2009)

Colloquium Mathematicae

We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.

Compactness conditions for elementary operators

Matej Brešar, Yuri V. Turovskii (2007)

Studia Mathematica

Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.

Compactness in the First Baire Class and Baire-1 Operators

Mercourakis, S., Stamati, E. (2002)

Serdica Mathematical Journal

For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M,...

Compactness of composition operators acting on weighted Bergman-Orlicz spaces

Ajay K. Sharma, S. Ueki (2012)

Annales Polonici Mathematici

We characterize compact composition operators acting on weighted Bergman-Orlicz spaces α ψ = f ∈ H ( ) : ∫ ψ ( | f ( z ) | ) d A α ( z ) < ∞ , where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition l i m t → ∞ ψ ( t ) / t = ∞ and the Δ₂-condition. In fact, we prove that C φ is compact on α ψ if and only if it is compact on the weighted Bergman space ² α .

Compactness of derivations from commutative Banach algebras

Matthew J. Heath (2010)

Banach Center Publications

We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally, we give...

Compactness of Hardy-type integral operators in weighted Banach function spaces

David Edmunds, Petr Gurka, Luboš Pick (1994)

Studia Mathematica

We consider a generalized Hardy operator T f ( x ) = ϕ ( x ) ʃ 0 x ψ f v . For T to be bounded from a weighted Banach function space (X,v) into another, (Y,w), it is always necessary that the Muckenhoupt-type condition ℬ = s u p R > 0 ∥ ϕ χ ( R , ∞ ) ∥ Y ∥ ψ χ ( 0 , R ) ∥ X ' < ∞ be satisfied. We say that (X,Y) belongs to the category M(T) if this Muckenhoupt condition is also sufficient. We prove a general criterion for compactness of T from X to Y when (X,Y) ∈ M(T) and give an estimate for the distance of T from the finite rank operators. We apply the results to Lorentz spaces and characterize...

Compactness of the integration operator associated with a vector measure

S. Okada, W. J. Ricker, L. Rodríguez-Piazza (2002)

Studia Mathematica

A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.

Compactness properties of Feller semigroups

G. Metafune, D. Pallara, M. Wacker (2002)

Studia Mathematica

We study the compactness of Feller semigroups generated by second order elliptic partial differential operators with unbounded coefficients in spaces of continuous functions in ℝ N .

Currently displaying 2001 – 2020 of 11135