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Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

T. Alvarez;  R. Cross;  A. Gouveia — 1995

Studia Mathematica

Characterisations are obtained for the following classes of unbounded linear operators between normed spaces: weakly compact, weakly completely continuous, and unconditionally converging operators. Examples of closed unbounded operators belonging to these classes are exhibited. A sufficient condition is obtained for the weak compactness of T' to imply that of T.

Relatively open operators and the ubiquitous concept.

R. W. Cross — 1994

Publicacions Matemàtiques

A linear operator T: D(T) ⊂ X → Y, when X and Y are normed spaces, is called (UO) if every infinite dimensional subspace M of D(T) contains another such subspace N for which T|N is open (in the relative sense). The following properties are shown to be equivalent: (i) T is UO, (ii) T is ubiquitously almost open, (iii) no infinite dimensional restriction of T is injective and precompact, (iv) either T is upper semi-Fredholm or T has finite dimensional range, (v) for each infinite dimensional subspace...

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