Spaces $X$ in which all prime $z$-ideals of $C(X)$ are minimal or maximal

Melvin Henriksen; Jorge Martinez; Grant R. Woods

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Displaying similar documents to “Spaces $X$ in which all prime $z$ -ideals of $C (X)$ are minimal or maximal”

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $D$ be a nonempty compact subset of a Banach space $X$ and denote by $S (X)$ the family of all nonempty bounded closed convex subsets of $X$ . We endow $S (X)$ with the Hausdorff metric and show that there exists a set $ℱ \subset S (X)$ such that its complement $S (X) ∖ ℱ$ is $σ$ -porous and such that for each $A \in ℱ$ and each $\tilde{x} \in D$ , the set of solutions of the best approximation problem $∥ \tilde{x} - z ∥ \to min$ , $z \in A$ , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

Some results on $L Σ (κ)$ -spaces

Fidel Casarrubias Segura, Oleg Okunev, Paniagua C. G. Ramírez (2008)

Commentationes Mathematicae Universitatis Carolinae

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We present several results related to $L Σ (κ)$ -spaces where $κ$ is a finite cardinal or $ω$ ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.

Non-compact perturbations of $m$ -accretive operators in general Banach spaces

Mieczysław Cichoń (1992)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we deal with the Cauchy problem for differential inclusions governed by $m$ -accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x^{'} (t) \in - A x (t) + f (t, x (t))$ , $x (0) = x_{0}$ , where $A$ is an $m$ -accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.

On the eigenvalues of a Robin problem with a large parameter

Alexey Filinovskiy (2014)

Mathematica Bohemica

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We consider the Robin eigenvalue problem $Δ u + λ u = 0$ in $Ω$ , $\partial u / \partial ν + α u = 0$ on $\partial Ω$ where $Ω \subset ℝ^{n}$ , $n \geq 2$ is a bounded domain and $α$ is a real parameter. We investigate the behavior of the eigenvalues $λ_{k} (α)$ of this problem as functions of the parameter $α$ . We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative $λ_{1}^{'} (α)$ . Assuming that the boundary $\partial Ω$ is of class $C^{2}$ we obtain estimates to the difference $λ_{k}^{D} - λ_{k} (α)$ between the $k$ -th eigenvalue of the Laplace operator with...

Displaying similar documents to “Spaces X in which all prime z -ideals of C ( X ) are minimal or maximal”

Best approximations and porous sets

Some results on L Σ ( κ ) -spaces

Non-compact perturbations of m -accretive operators in general Banach spaces

On the eigenvalues of a Robin problem with a large parameter

Displaying similar documents to “Spaces $X$ in which all prime $z$ -ideals of $C (X)$ are minimal or maximal”

Some results on $L Σ (κ)$ -spaces

Non-compact perturbations of $m$ -accretive operators in general Banach spaces