scholarly journals Hermitian spectral theory, automatic continuity and locally convex ∗-algebras with a C∗-enveloping algebra

2007 ◽  
Vol 331 (1) ◽  
pp. 69-90
Author(s):  
Subhash J. Bhatt ◽  
Maria Fragoulopoulou ◽  
Atsushi Inoue ◽  
Dinesh J. Karia
Keyword(s):  
Spectral Theory ◽  
Automatic Continuity ◽  
Enveloping Algebra ◽  
Locally Convex Algebras ◽  
Locally Convex

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.

On C*-Like Locally Convex ∗-Algebras

2002 ◽  
Vol 235 (1) ◽  
pp. 51-58 ◽  
Author(s):  
Atsushi Inoue ◽  
Klaus-Detlef Kürsten
Keyword(s):  
Locally Convex Algebras ◽  
Locally Convex

scholarly journals Köthe coechelon spaces as locally convex algebras

2010 ◽  
Vol 199 (3) ◽  
pp. 241-265 ◽  
Author(s):  
José Bonet ◽  
Paweł Domański
Keyword(s):  
Locally Convex Algebras ◽  
Locally Convex

Spectral and Boundedness Radii in Locally Convex Algebras

1998 ◽  
Vol 5 (3) ◽  
pp. 233-241
Author(s):  
A. El Kinani ◽  
L. Oubbi ◽  
M. Oudadess
Keyword(s):  
Spectral Radius ◽  
Locally Convex Algebras ◽  
Locally Convex

Abstract Connections between the spectral radius and the radius of boundedness are studied. Different characterizations of algebras (Q-property, strong saquentiality) are given in terms of these radii. Examples and applications are also provided.

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