A new technique for proving fixed-point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded group representation in a real or complex Hilbert space is orthogonaliza...

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Let X be a Banach space. Given a subset A of the dual space X* denote by $A_{(1)}$ the weak* sequential closure of A, i.e., the set of all limits of weak*-convergent sequences in A. The study of weak* sequential closures of linear subspaces of the du...

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists a projecti...

We consider real spaces only. Definition. An operator $T:X\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving extension $\t...

A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is orthogonalizable or...