Displaying similar documents to “Perturbation of strongly continuous cosine family generators”

Absolutely strongly star-Hurewicz spaces

Yan-Kui Song (2015)

Open Mathematics

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A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.

Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space

Adam Bobrowski, Wojciech Chojnacki (2013)

Studia Mathematica

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We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets...

Remarks on strongly star-Menger spaces

Yan-Kui Song (2013)

Commentationes Mathematicae Universitatis Carolinae

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A space X is strongly star-Menger if for each sequence ( 𝒰 n : n ) of open covers of X , there exists a sequence ( K n : n N ) of finite subsets of X such that { S t ( K n , 𝒰 n ) : n } is an open cover of X . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.

Strongly continuous integrated C-cosine operator functions

Shen Wang, Zhen Huang (1997)

Studia Mathematica

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We extend some recent results for regularized semigroups to strongly continuous n-times integrated C-cosine operator functions. Several equivalent conditions for the existence and uniqueness of solutions of (ACP 2 ) are also presented.