Cohomology of Banach algebras of operators and geometry of Banach spaces

2007 ◽  
pp. 57-80
Author(s):  
Ariel Blanco ◽  
Niels Grønbæk
Keyword(s):  
Banach Spaces ◽  
Banach Algebras

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

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.

Representation of Banach Algebras with an Involution

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.

scholarly journals Spectral integration and spectral theory for non-Archimedean Banach spaces

2002 ◽  
Vol 31 (7) ◽  
pp. 421-442 ◽  
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.

scholarly journals Module bundles and module amenability

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.

scholarly journals DISCUSSIONS ON PARTIAL ISOMETRIES IN BANACH SPACES AND BANACH ALGEBRAS

2017 ◽  
Vol 54 (2) ◽  
pp. 485-495
Author(s):  
Abdulla Alahmari ◽  
Mohamed Mabrouk ◽  
Mohamed Aziz Taoudi
Keyword(s):  
Banach Spaces ◽  
Banach Algebras ◽  
Partial Isometries

scholarly journals Small isomorphisms between operator algebras

1985 ◽  
Vol 28 (2) ◽  
pp. 121-131 ◽  
Author(s):  
Krzysztof Jarosz
Keyword(s):  
Banach Spaces ◽  
Operator Algebras ◽  
Banach Algebras ◽  
The Other ◽  
Linear Map ◽  
Other Hand ◽  
Function Algebras

Let A and B be function algebras. The well-known Nagasawa theorem [5] states that A and B are isometric if and only if they are isomorphic in the category of Banach algebras. In [2] it was shown that this theorem is stable in the sense that if the Banach–Mazur distance between the underlying Banach spaces of A and B is close to one then these algebras are almost isomorphic, that is there exists a linear map T from A onto B such that . On the other hand one can get from Theorems 1 and 3 of [3] that the Nagasawa theorem can be extended to some operator algebras as follows:

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