Displaying similar documents to “Unbounded linear transformations of upper semi-Fredholm type in normed spaces”

Relatively open operators and the ubiquitous concept.

R. W. Cross (1994)

Publicacions Matemàtiques

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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...

On inessential and improjective operators.

Pietro Aiena, Manuel González (1998)

Studia Mathematica

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We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of...

Hereditarily finitely decomposable Banach spaces

V. Perenczi (1997)

Studia Mathematica

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A Banach space is said to be H D n if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of H D n spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex H D n , then dim ( ( X ) / S ( X ) ) n 2 , where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic...