Displaying similar documents to “On strongly closed subalgebras of B(X)”

Strongly compact algebras.

Miguel Lacruz, Victor Lomonosov, Luis Rodríguez Piazza (2006)

RACSAM

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An algebra of bounded linear operators on a Hilbert space is said to be if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras are established....

Strong proximinality and polyhedral spaces.

Gilles Godefroy, V. Indumathi (2001)

Revista Matemática Complutense

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In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.

Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

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We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter h ∈ Ω ⊂ ℝ m . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.