Köthe dual of Banach sequence spaces $\ell _p[X]$$(1\le p<\infty )$ and Grothendieck space

Cong Xin Wu; Qing Ying Bu

Displaying similar documents to “Köthe dual of Banach sequence spaces $ℓ_{p} [X]$ $(1 \leq p < \infty)$ and Grothendieck space”

Extensions of linear operators from hyperplanes of $l_{\infty}^{(n)}$

Marco Baronti, Vito Fragnelli, Grzegorz Lewicki (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let $Y \subset l_{\infty}^{(n)}$ be a hyperplane and let $A \in ℒ (Y)$ be given. Denote $\begin{matrix} 𝒜 = & {L \in ℒ (l_{\infty}^{(n)}, Y) : L ∣ Y = A} and & λ_{A} = inf {∥ L ∥ : L \in 𝒜} . \end{matrix}$ In this paper the problem of calculating of the constant $λ_{A}$ is studied. We present a complete characterization of those $A \in ℒ (Y)$ for which $λ_{A} = ∥ A ∥$ . Next we consider the case $λ_{A} > ∥ A ∥$ . Finally some computer examples will be presented.

On the convergence of certain sums of independent random elements

Juan Carlos Ferrando (2002)

Commentationes Mathematicae Universitatis Carolinae

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In this note we investigate the relationship between the convergence of the sequence ${S_{n}}$ of sums of independent random elements of the form $S_{n} = \sum_{i = 1}^{n} ε_{i} x_{i}$ (where $ε_{i}$ takes the values $\pm 1$ with the same probability and $x_{i}$ belongs to a real Banach space $X$ for each $i \in ℕ$ ) and the existence of certain weakly unconditionally Cauchy subseries of $\sum_{n = 1}^{\infty} x_{n}$ .

On the classes of hereditarily $ℓ_{p}$ Banach spaces

Parviz Azimi, A. A. Ledari (2006)

Czechoslovak Mathematical Journal

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Let $X$ denote a specific space of the class of $X_{α, p}$ Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily $ℓ_{p}$ Banach spaces. We show that for $p > 1$ the Banach space $X$ contains asymptotically isometric copies of $ℓ_{p}$ . It is known that any member of the class is a dual space. We show that the predual of $X$ contains isometric copies of $ℓ_{q}$ where $\frac{1}{p} + \frac{1}{q} = 1$ . For $p = 1$ it is known that the predual of the Banach space $X$ contains asymptotically isometric copies of...

Antiproximinal sets in the Banach space $c (X)$

S. Cobzaş (1997)

Commentationes Mathematicae Universitatis Carolinae

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If $X$ is a Banach space then the Banach space $c (X)$ of all $X$ -valued convergent sequences contains a nonvoid bounded closed convex body $V$ such that no point in $C (X) ∖ V$ has a nearest point in $V$ .

Displaying similar documents to “Köthe dual of Banach sequence spaces ℓ p [ X ] ( 1 ≤ p < ∞ ) and Grothendieck space”

Extensions of linear operators from hyperplanes of l ∞ ( n )

On the convergence of certain sums of independent random elements

On the classes of hereditarily ℓ p Banach spaces

Antiproximinal sets in the Banach space c ( X )

Displaying similar documents to “Köthe dual of Banach sequence spaces $ℓ_{p} [X]$ $(1 \leq p < \infty)$ and Grothendieck space”

Extensions of linear operators from hyperplanes of $l_{\infty}^{(n)}$

On the classes of hereditarily $ℓ_{p}$ Banach spaces

Antiproximinal sets in the Banach space $c (X)$