An extension theorem for D-normal spaces

The Hopf Extension Theorem for Topological Spaces

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

An Extension of the Marcinkiewicz Interpolation Theorem to Lorentz Spaces

V J o v J t f(y) ) " ) 7 V J o ~ ) • Third, previously open questions concerning the Marcinkiewicz Theorem are settled by showing our result is best possible. Consider complex-valued, measurable functions ƒ defined on a measure space (ikf, m). The distribution function of ƒ is defined by (2) X(y) = X/GO =m{xeM:\ ƒ(*) | > y}, y > 0. X(y) is nonincreasing and continuous from the right. The noninc...

An Extension of Elton’s `1 Theorem to Complex Banach Spaces

Let ε > 0 be sufficiently small. Then, for θ = 0.225 √ ε, there exists δ := δ(ε) < 1 such that if (ei) n i=1 are vectors in the unit ball of a complex Banach space X which satisfy