DISCUSSIONS ON PARTIAL ISOMETRIES IN BANACH SPACES AND BANACH ALGEBRAS

Abdulla Alahmari; Mohamed Mabrouk; Mohamed Aziz Taoudi

doi:10.4134/bkms.b160055

Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

Applied General Topology ◽

10.4995/agt.2020.12220 ◽

2020 ◽

Vol 21 (1) ◽

pp. 135

Author(s):

Godwin Amechi Okeke ◽

Mujahid Abbas

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Banach Spaces ◽

Nonlinear Integral Equation ◽

Metric Spaces ◽

Banach Algebras ◽

Cone Metric Spaces ◽

Nonlinear Operators ◽

Complex Valued ◽

Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

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Representation of Banach Algebras with an Involution

Canadian Journal of Mathematics ◽

10.4153/cjm-1957-051-8 ◽

1957 ◽

Vol 9 ◽

pp. 435-442

Author(s):

J. A. Schatz

Keyword(s):

Hilbert Space ◽

Banach Spaces ◽

Banach Algebras ◽

Bounded Operators ◽

Uniformly Closed

In 1943 Gelfand and Neumark (3) characterized uniformly closed self-adjoint algebras of bounded operators on a Hilbert space as Banach algebras with an involution (a conjugate linear anti-isomorphism of period two) satisfying several additional conditions. The main purpose of this paper is to point out that if we consider algebras of bounded operators on complex Banach spaces more general than Hilbert space, then we can represent a larger class of algebras by essentially the same methods.

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Spectral integration and spectral theory for non-Archimedean Banach spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120201150x ◽

2002 ◽

Vol 31 (7) ◽

pp. 421-442 ◽

Cited By ~ 8

Author(s):

S. Ludkovsky ◽

B. Diarra

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Banach Algebras ◽

Linear Operators ◽

Spectral Integration ◽

Different Types ◽

Commutative Subalgebras ◽

Continuous Operators ◽

Stone Theorem ◽

Continuous Linear Operators

Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.

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Module bundles and module amenability

Acta et Commentationes Universitatis Tartuensis de Mathematica ◽

10.12697/acutm.2021.25.08 ◽

2021 ◽

Vol 25 (1) ◽

pp. 119-141

Author(s):

Terje Hill ◽

David A. Robbins

Keyword(s):

Banach Spaces ◽

Compact Hausdorff Space ◽

Hausdorff Space ◽

Banach Algebras ◽

Module Amenability

Let X be a compact Hausdorff space, and let {Ax : x ∈ X} and {Bx : x ∈ X} be collections of Banach algebras such that each Ax is a Bx-bimodule. Using the theory of bundles of Banach spaces as a tool, we investigate the module amenability of certain algebras of Ax-valued functions on X over algebras of Bx-valued functions on X.

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On a Generalization of Partial Isometries in Banach Spaces

Georgian Mathematical Journal ◽

10.1515/gmj.2008.177 ◽

2008 ◽

Vol 15 (1) ◽

pp. 177-188

Author(s):

Mohamed Aziz Taoudi

Keyword(s):

Banach Spaces ◽

Hilbert Spaces ◽

Natural Generalization ◽

Partial Isometries ◽

Basic Properties

Abstract This paper is concerned with the definition and study of semipartial isometries on Banach spaces. This class of operators, which is a natural generalization of partial isometries from Hilbert to general Banach spaces, contains in particular the class of partial isometries recently introduced by M. Mbekhta [Acta Sci. Math. (Szeged) 70: 767–781, 2004]. First of all, we establish some basic properties of semi-partial isometries. Next, we introduce the notion of pseudo Moore–Penrose inverse as a natural generalization of the Moore–Penrose inverse from Hilbert spaces to arbitrary Banach spaces. This concept is used to carry out a classification for semi-partial isometries in Banach spaces and to provide a characterization for Hilbert spaces.

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