then X*, is said to be optimal. A typical choice for Y{ is the image of a unit ball of some normed linear space Y (which may be different from X) under a compact linear mapping K of Y into X. Thus, Y{= {Ky: ]]y][v =< 1}. When X = Y is a Hilbert space, then it is possible to obtain an expression for d,(Y{'; X) and identify optimal subspaces. These facts originated with the example given by Kolmo...

A group G given by a presentation G = 〈A ‖ R〉 is called weakly finitely presented if every finitely generated subgroup of G, generated by (images of) some words in A, is naturally isomorphic to the subgroup of a group G0 = 〈A0 ‖ R0〉, where A0 ⊆ A, R0 ⊆ R are finite, generated by (images of) the same words. In the article, weakly finitely presented periodic groups which are not locally finite ar...

For a compact Hausdorff space X , the space SC(X ×X) of separately continuous complex valued functions on X can be viewed as a C∗-subalgebra of C(X)∗∗⊗C(X)∗∗, namely those elements which slice into C(X). The analogous definition for a non-commutative C∗-algebra does not necessarily give an algebra, but we show that there is always a greatest C∗-subalgebra. This thus gives a noncommutative notio...

For a weakly exact magnetic flows with a bounded primitive on a closed Riemannian manifold, we prove the existence of periodic orbits in almost all energy levels below of the Mañé’s critical value. Mathematics Subject Classification: 37J45