scholarly journals Subsets of nonempty joint spectrum in topological algebras

2018 ◽  
Vol 143 (4) ◽  
pp. 441-448
Author(s):  
Antoni Wawrzyńczyk
Keyword(s):  
Topological Algebras ◽  
Joint Spectrum

scholarly journals About the joint spectrum of vector-valued functions

2020 ◽  
Vol 24 (1) ◽  
pp. 147-158
Author(s):  
Mart Abel
Keyword(s):  
Banach Algebras ◽  
Topological Algebras ◽  
Joint Spectrum ◽  
Vector Valued Functions ◽  
Vector Valued

We generalize the results of Abtahi and Farhangi about the joint spectrum and A-valued spectrum of a vector-valued map from the class of unital commutative semisimple Banach algebras to the case of unital topological algebras.

scholarly journals Joint Spectra of Generators in Topological Algebras

2007 ◽  
Vol 2007 ◽  
pp. 1-7
Author(s):  
Antoni Wawrzyńczyk
Keyword(s):  
Topological Algebra ◽  
Topological Algebras ◽  
Joint Spectrum ◽  
Multiplicative Functionals

Let𝒜be a complex topological algebra with unit 1 and𝒰a family of proper closed ideals in𝒜. For an arbitraryS⊂𝒜we define a globally defined joint spectrumσ𝒰(S)={(λs)s∈S∈ℂS  |  ∃ I  ∈𝒰(s−λs)∈I ∀s∈S}. We prove that forSgenerating𝒜the spectrumσ𝒰(S)can be identified with the set𝔐𝒰of continuous multiplicative functionalsfon𝒜such that kerf∈𝒰. The relation is given by the formulaσ𝒰(S)={(f(s))s∈S  |   f∈𝔐𝒰}. If𝒜is aQ-algebra, the setσ𝒰(S)is rationally convex.

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

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