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For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.

A note on the range of the operator $X \mapsto T X - X T$ defined on $𝒞_{2} (ℋ)$ .

Lauric, Vasile (2009)

International Journal of Mathematics and Mathematical Sciences

A note on the stability of linear combinations of algebraic operators.

I. Chalendar, E. Fricain, D. Timotin (2008)

Extracta Mathematicae

A quantified Tauberian theorem for sequences

David Seifert (2015)

Studia Mathematica

The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by the author...

A remark on the d-characteristic and the $d_{Ξ}$ -characteristic of linear operators in a Banach space

Štefan Schwabik (1973)

Studia Mathematica

A topological characterization of the product of two closed operators

Bekkai Messirdi, Mohammed Hichem Mortad, Abdelhalim Azzouz, Ghouti Djellouli (2008)

Colloquium Mathematicae

The purpose of this work is to give a topological condition for the usual product of two closed operators acting in a Hilbert space to be closed.

Absolutely P-Summing, P-Nuclear Operators and Their Conjugates.

Joel S. Cohen (1973)

Mathematische Annalen

Additive combinations of special operators

Pei Wu (1994)

Banach Center Publications

This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible operators...

Adjoint domains and generalized splines

Richard C. Brown (1975)

Czechoslovak Mathematical Journal

Adjungiertenbildungen in der Operatortheorie.

G. Hetzer, J. Reinermann (1974/1975)

Jahresbericht der Deutschen Mathematiker-Vereinigung

Algebraic analysis in structures with the Kaplansky-Jacobson property

D. Przeworska-Rolewicz (2005)

Studia Mathematica

In 1950 N. Jacobson proved that if u is an element of a ring with unit such that u has more than one right inverse, then it has infinitely many right inverses. He also mentioned that I. Kaplansky proved this in another way. Recently, K. P. Shum and Y. Q. Gao gave a new (non-constructive) proof of the Kaplansky-Jacobson theorem for monoids admitting a ring structure. We generalize that theorem to monoids without any ring structure and we show the consequences of the generalized Kaplansky-Jacobson...

Algebraic and topological selections of multi-valued linear relations

Sung J. Lee, M. Zuhair Nashed (1990)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Almost exactness in normed spaces II

Robin Harte, Мostafa Мbekhta (1996)

Studia Mathematica

In the normed space of bounded operators between a pair of normed spaces, the set of operators which are "bounded below" forms the interior of the set of one-one operators. This note is concerned with the extension of this observation to certain spaces of pairs of operators.

Almost regular operators are regular.

Teresa Bermúdez, Manuel González (1999)

Extracta Mathematicae

An Atkinson-type theorem for B-Fredholm operators

M. Berkani, M. Sarih (2001)

Studia Mathematica

Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only if its projection...

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