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Weakly continuous functions of Baire class 1.

T. S. S. R. K. Rao — 2000

Extracta Mathematicae

For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {f} contained in C(K,X) (space of norm continuous functions) such that f --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.

Some generalizations of Kadison's theorem: a survey.

T. S. S. R. K. Rao — 2004

Extracta Mathematicae

Motivated by a well-known result of Kadison that describes surjective isometries of the space of compact and the space of bounded operators on a Hilbert space, in this paper we investigate the structure of surjective isometries on the space of compact and on the space of bounded operators between Banach spaces. We give an example to show that isometries in general need not be of the canonical form. As an application of our study of the group of isometries, we consider the algebraic reflexivity of...

Boundedness of linear maps

T. S. S. R. K. Rao — 2000

Commentationes Mathematicae Universitatis Carolinae

In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.

Transitivity of proximinality and norm attaining functionals

Darapaneni NarayanaT. S. S. R. K. Rao — 2006

Colloquium Mathematicae

We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in R ( 1 ) ˜ spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and...

Ball remotal subspaces of Banach spaces

Pradipta BandyopadhyayBor-Luh LinT. S. S. R. K. Rao — 2009

Colloquium Mathematicae

We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X).

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