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Idempotents dans les algèbres de Banach

100%

Berkani M.

Studia Mathematica

1996

tom 120

nr 2

155-158

Using the holomorphic functional calculus we give a characterization of idempotent elements commuting with a given element in a Banach algebra.

Range projections of idempotents in C*-algebras

80%

Koliha J.

2001

tom Vol. 34, nr 1

91-103

In this paper we study range projections of idempotents m C*-algebras, and use them to obtain a Schur type decomposition that leads to simple proofs of results on Moore-Penrose inverse and norms of idempotents. We analyze the continuity of range projections, obtain a general result on their approximation, and recover a result of Vidav on two projections in a Hilbert space. Several representations of range projections are given.

Convergence of orthogonal series of projections in Banach spaces

80%

Jajte R. , Paszkiewicz A.

1997

tom 66

nr 1

137-153

For a sequence $(A_j)$ of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums $S_n = ∑^n_{j=1} A_j$ in a "strong" sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of $S_n$ (i.e. $S_{n}f → Af$ μ-a.e. for all f ∈ 𝓓(A)).

On the maximal subsemigroups of the semigroup of all monotone transformations

60%

Gyudzhenov I. , Dimitrova I.

Discussiones Mathematicae - General Algebra and Applications

2006

tom 26

nr 2

199-217

In this paper we consider the semigroup Mₙ of all monotone transformations on the chain Xₙ under the operation of composition of transformations. First we give a presentation of the semigroup Mₙ and some propositions connected with its structure. Also, we give a description and some properties of the class $J̃_{n-1}$ of all monotone transformations with rank n-1. After that we characterize the maximal subsemigroups of the semigroup Mₙ and the subsemigroups of Mₙ which are maximal in $J̃_{n-1}$.