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Displaying 21 – 40 of 154

Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

Francisco Javier Pérez Fernández, F. Benítez-Trujillo, Antonio Aizpuru Tomás (2000)

Czechoslovak Mathematical Journal

In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space $X$ can be characterized through the behaviour of its weakly- $*$ unconditionally Cauchy series in $X^{*}$ .

Characterizations of series in Banach spaces.

Aizpuru, A., Pérez-Fernández, F.J. (1999)

Acta Mathematica Universitatis Comenianae. New Series

Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet, A. Defant, A. Peris, M. Ramanujan (1994)

Studia Mathematica

We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from $l_{p}$ to $l_{q}$ . Several sharp forms of this result are also included.

Combinatorial inequalities and subspaces of L₁

Joscha Prochno, Carsten Schütt (2012)

Studia Mathematica

Let M₁ and M₂ be N-functions. We establish some combinatorial inequalities and show that the product spaces $ℓ ⁿ_{M ₁} (ℓ ⁿ_{M ₂})$ are uniformly isomorphic to subspaces of L₁ if M₁ and M₂ are “separated” by a function $t^{r}$ , 1 < r < 2.

Commutative, radical amenable Banach algebras

C. Read (2000)

Studia Mathematica

There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector $y_{1}$ ; then approximate...

Complex Convexity of Orlicz-Lorentz Spaces and its Applications

Changsun Choi, Anna Kamińska, Han Ju Lee (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz-Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from $d *_{(} w, 1)$ into d(w,1), where $d *_{(} w, 1)$ is a predual of a complex Lorentz sequence space d(w,1), if and only if wi ∈ c₀∖ℓ₂.

Computing discrete convolutions with verified accuracy via Banach algebras and the FFT

Jean-Philippe Lessard (2018)

Applications of Mathematics

We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed $ℓ^{1}$ Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori...

Concerning holomorphy types for Banach spaces

Leopoldo Nachbin (1970)

Studia Mathematica

Continuity of superposition operators on $w_{0}$ and $W_{0}$

Ryszard Płuciennik (1990)

Commentationes Mathematicae Universitatis Carolinae

Continuous restrictions of linear functionals

Béla Bollobás, Imre Leader (1992)

Acta Universitatis Carolinae. Mathematica et Physica

Contractive projections in Orlicz sequence spaces.

Randrianantoanina, Beata (2004)

Abstract and Applied Analysis

Copies of $l^{1}$ and $c_{o}$ in Musielak-Orlicz sequence spaces

Ghassan Alherk, Henryk Hudzik (1994)

Commentationes Mathematicae Universitatis Carolinae

Criteria in order that a Musielak-Orlicz sequence space $l^{Φ}$ contains an isomorphic as well as an isomorphically isometric copy of $l^{1}$ are given. Moreover, it is proved that if $Φ = (Φ_{i})$ , where $Φ_{i}$ are defined on a Banach space, $X$ does not satisfy the $δ_{2}^{o}$ -condition, then the Musielak-Orlicz sequence space $l^{Φ} (X)$ of $X$ -valued sequences contains an almost isometric copy of $c_{o}$ . In the case of $X = I R$ it is proved also that if $l^{Φ}$ contains an isomorphic copy of $c_{o}$ , then $Φ$ does not satisfy the $δ_{2}^{o}$ -condition. These results extend some...

Copies of Orlicz sequences spaces in the interpolation spaces ${\bar{A}}_{ρ, Φ}$ .

Echandía, Ventura, Hernández, Jorge (2008)

Divulgaciones Matemáticas

Correction to the paper: Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm

Henryk Hudzik, Yi Ning Ye (1994)

Commentationes Mathematicae Universitatis Carolinae

Criteria for $k_{M} < \infty$ in Musielak-Orlicz spaces

Lianying Cao, Ting Fu Wang (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper, some necessary and sufficient conditions for $sup {k_{x} : ∥ x ∥^{0} = 1} < \infty$ in Musielak-Orlicz function spaces as well as in Musielak-Orlicz sequence spaces are given.

Diagonal nuclear operators

L. Crone, D. Fleming, P. Jessup (1972)

Studia Mathematica

Differentiability of Musielak-Orlicz sequence spaces

Ryszard Płuciennik, Yi Ning Ye (1989)

Commentationes Mathematicae Universitatis Carolinae

Distinguished subspaces of $L_{p}$ of maximal dimension

Geraldo Botelho, Daniel Cariello, Vinícius V. Fávaro, Daniel Pellegrino, Juan B. Seoane-Sepúlveda (2013)

Studia Mathematica

Dunford-Pettis-like properties of projective and natural tensor product spaces.

Jesús M. Fernández Castillo, Juan A. López Molina (1993)

Revista Matemática de la Universidad Complutense de Madrid

Several properties of weakly p-summable sequences and of the scale of p-converging operators (i.e., operators transforming weakly p-summable sequences into convergent sequences) in projective and natural tensor products with an lp space are considered. The last section studies the Dunford-Pettis property of order p (i.e., every weakly compact operator is p-convergent) in those spaces.

Eigenvalue distribution of integral operators defined by Orlicz kernels.

Elshobaky, E., Faragallah, M. (1998)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Currently displaying 21 – 40 of 154

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