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17 results on '"Pluciennik, Ryszard"'

1. On some modifications of n-th von Neumann-Jordan constant for banach spaces

Author

Ciesielski, Maciej and Płuciennik, Ryszard

Subjects
Mathematics - Functional Analysis, 46E30, 46E40, 46B20
Abstract

There are discussed some modifications of n-th von Neumann-Jordan constant considered by M. Kato, Y. Takahashi and K. Hashimoto. We study, among others, upper, lower, upper modified and lower modified n-th von Neumann-Jordan constant and relationships between them. There are characterized uniformly non-l_{n}^{1} Banach spaces in terms of the upper modified n-th von Neumann-Jordan constant. Moreover, this constant is calculated explicitly for Lebesgue spaces L^{p} and l^{p} (1\leq p\leq oo)., Comment: 18 pages

Published
2018

2. On some modifications of n-th von Neumann–Jordan constant for Banach spaces

Author

Ciesielski, Maciej and Pluciennik, Ryszard

Abstract

We study, among others, upper, lower, upper modified and lower modified n-th von Neumann–Jordan constant and relationships between them. There are characterized uniformly non-ln1Banach spaces in terms of the upper modified n-th von Neumann–Jordan constant. Moreover, this constant is calculated explicitly for Lebesgue spaces Lpand lp(1=p=8).Finally, it is shown that the sequence of n-th upper and modified upper von Neumann–Jordan constants for the space Lpas well as lp(2

Published
2024
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11. $P$-convexity of Musielak-Orlicz sequence spaces of Bochner type

Author

Kolwicz, Pawel and Pluciennik, Ryszard

Abstract

It is proved that the Musielak-Orlicz sequence space $l_\varphi(X)$ of Bochner type is $\texttt{P}$-convex if and only if both spaces $l_\varphi(\mathbb{R})$ and $X$ are $\texttt{P}$-convex. In particular, the Lebesgue-Bochner sequence space $l^p(X)$ is $\texttt{P}$-convex if $X$ is $\texttt{P}$-convex and $1 < p

Published
1997

17. Banach-Saks Property and Property (β) in Cesàro Sequence Spaces.

Author

Cui, Yunan, Meng, Chenghui, and PLuciennik, Ryszard

Subjects
*BANACH spaces, *SEQUENCE spaces
Abstract

Abstract. A new constant C(X) for any Banach space X is introduced. It is proved that C(X) < 2 implies the weak Banach-Saks property for the space X. In particular, C(ces[sub p]) is found for Cesaro sequence space ces[sub p] (1 < p < Infinity). Moreover, it is shown that thc space ces[sub p] (1 < p < infinity) has property (beta). [ABSTRACT FROM AUTHOR]

Published
2000
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