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A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if $𝒳$ is a Banach space such that $𝒳^{*}$ has a SRBF, then $𝒳$ has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space $𝒳$ has an approximative Schauder frame, then $𝒳^{*}$ has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.

On the existence of Schauder bases in Sobolev spaces

Svatopluk Fučík, Oldřich John, Jindřich Nečas (1972)

Commentationes Mathematicae Universitatis Carolinae

On the Existence of Sub-Markovian Resolvents.

J.C. Taylor (1972)

Inventiones mathematicae

On the existence of traces of distributions belonging to $B_{p, ϑ}^{(k)}$ (Preliminary communication)

Jan Kadlec (1965)

Commentationes Mathematicae Universitatis Carolinae

On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.

V. Losert (1979)

Monatshefte für Mathematik

On the existence of unitary representations of commutative nuclear Lie groups

Wojciech Banaszczyk (1983)

Studia Mathematica

On the existence of universal ...-nuclear Fréchet spaces.

V.B. Moscatelli (1978)

Journal für die reine und angewandte Mathematik

On the existence problem in the algebraic approach to quantum field theory

Hofmann, Gerald (1979)

Abstracta. 7th Winter School on Abstract Analysis

On the expansion theorem described by $H (A, B)$ spaces.

El-Sabbagh, A.A. (2004)

International Journal of Mathematics and Mathematical Sciences

On the expected value of vector lattice-valued random variables

Rastislav Potocký (1986)

Mathematica Slovaca

On the exponential of a bounded linear operator in a L(E,E) algebra

Freire, Nuno C. (1991)

Portugaliae mathematica

On the exponential Orlicz norms of stopped Brownian motion

Goran Peškir (1996)

Studia Mathematica

Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by $ψ_{p} (x) = {e x p (| x |}^{p}) - 1$ with 0 < p ≤ 2) of $m a x_{0 \leq t \leq τ} | B_{t} |$ or $| B_{τ} |$ to be finite, where $B = {(B_{t})}_{t \geq 0}$ is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that $∥ m a x_{0 \leq t \leq τ} | B_{t} | ∥_{ψ_{1}} < \infty$ as soon as $E (τ^{k}) = O (C^{k} k^{k})$ for some constant C > 0 as k → ∞ (or equivalently $∥ τ ∥_{ψ_{1}} < \infty$ ). In particular, if τ ∼ Exp(λ) or $| N (0, σ^{2}) |$ then the last condition is satisfied, and we obtain $∥ m a x_{0 \leq t \leq τ} | B_{t} | ∥_{ψ_{1}} \leq K \sqrt E (τ)$ with some universal constant K > 0....

On the Extension of Continuous Linear Functionals and Best Approximation in Normed Linear Spaces.

I. SINGER (1965)

Mathematische Annalen

On the extension of continuous linear maps in function spaces and the splitness of Dolbeaut complexes of holomorphic Banach bundles

Khue Nguyen (1982)

Studia Mathematica

On the extension of holomorphic functions on a locally convex space

Nguyen Van Khue (1983)

Annales Polonici Mathematici

On the extension of holomorphic maps on locally convex spaces with values in Fréchet spaces

Nguyen Van Khue (1984)

Annales Polonici Mathematici

Currently displaying 1221 – 1240 of 1952

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