-absolutely summing operators on the space and applications.
A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces
We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
A C(K) Banach space which does not have the Schroeder-Bernstein property
We construct a totally disconnected compact Hausdorff space K₊ which has clopen subsets K₊” ⊆ K₊’ ⊆ K₊ such that K₊” is homeomorphic to K₊ and hence C(K₊”) is isometric as a Banach space to C(K₊) but C(K₊’) is not isomorphic to C(K₊). This gives two nonisomorphic Banach spaces (necessarily nonseparable) of the form C(K) which are isomorphic to complemented subspaces of each other (even in the above strong isometric sense), providing a solution to the Schroeder-Bernstein problem for Banach spaces...
A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A class of special Hardy-Orlicz spaces and the space of BMOA functions
A density theorem.
A formula for the Bloch norm of a -function on the unit ball of
For a -function on the unit ball we define the Bloch norm by where is the invariant derivative of and then show that
A function space C(K) not weakly homeomorphic to C(K)×C(K)
A generalization of Signorini's perturbation method suggested by two problems of Grioli
A generalization of the Banach-Stone theorem
A Holsztyński theorem for spaces of continuous vector-valued functions
A Kronecker theorem in functional analysis
A local Bernstein inequality on real algebraic varieties.
A necessary and sufficient condition for existence of extremal functions of a linear functional on .
A nonlinear operator in potential theory
A Norm Preserving Complex Choquet Theorem.
A Normed Linear Space Containing the Schlicht Functions.
A Note on compactness in Banach spaces.
A note on nonfragmentability of Banach spaces.