Representable extensions of positive functionals and hermitian Banach *-algebras

2019 ◽  
Vol 158 (1) ◽  
pp. 66-86
Author(s):  
Zs. Szűcs ◽  
B. Takács
Keyword(s):  
Banach Algebras ◽  
Positive Functionals

Positive Functionals and Representations of Tensor Products of Symmetric Banach Algebras

1968 ◽  
Vol 20 ◽  
pp. 1192-1202 ◽  
Author(s):  
Harvey A. Smith
Keyword(s):  
Weak Topology ◽  
Banach Algebras ◽  
Tensor Products ◽  
Symmetric Algebra ◽  
Positive Functionals ◽  
Symmetric Banach Algebras

Except for using “algebra” rather than “ring” and “compact” rather than “bicompact”, we adopt the terminology used in (6). Every symmetric algebra, Ai, will have an identity, ei All representations will be cyclic and symmetric. Sets of functionals will carry the relative weak* topology.

scholarly journals Automatic continuity of positive functionals on topological involution algebras

1981 ◽  
Vol 23 (2) ◽  
pp. 265-281 ◽  
Author(s):  
P.G. Dixon
Keyword(s):  
Banach Algebra ◽  
Spectral Theory ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Automatic Continuity ◽  
Topological Algebras ◽  
Positive Functional ◽  
Open Questions ◽  
Positive Functionals ◽  
Locally Convex

This paper surveys the known results on automatic continuity of positive functionals on topological *-algebras and then shows how two theorems on Banach *-algebras extend to complete metrizable topological *-algebras. The two theorems concerned are Loy's theorem on separable Banach *-algebras A with centre Z such that AZ is of countable codimension and Varopoulos' result on Banach *-algebras with bounded approximate identity. Both theorems have the conclusion that all positive functionals on such algebras are continuous. The extension of the second theorem requires the algebra to be locally convex and the approximate identity to be ‘uniformly bounded’. Neither extension requires the algebra to be LMC. This means that the proof of the first theorem is quite different from the corresponding Banach algebra result (which used spectral theory). The proof of the second is closer to the previously known LMC version, but actually neater by being more general. It is also shown that the well-known estimate of |f(a*ba)| for a positive functional f on a Banach *-algebra may be obtained without the usual use of spectral theory. The paper concludes with a list of open questions.

Extreme Points of Positive Functionals and Spectral States on Real Banach Algebras

1992 ◽  
Vol 44 (4) ◽  
pp. 856-866
Author(s):  
Anand Srivastav
Keyword(s):  
Maximal Ideal ◽  
Short Proof ◽  
Banach Algebras ◽  
Extreme Points ◽  
Ideal Space ◽  
Shilov Boundary ◽  
Commutative Banach Algebras ◽  
Multiplicative Functionals ◽  
Positive Functionals ◽  
Spectral States

AbstractExtreme points of positive functionals and spectral states on real commutative Banach algebras are investigated and characterized as multiplicative functionals extending the well-known results from complex to real Banach algebras. As an application a new and short proof of the existence of the Shilov boundary of a real commutative Banach algebra with nonempty maximal ideal space is given.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

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