Infinite-Dimensional Grassmann-Banach Algebra

2004 ◽  
pp. 201-201
Author(s):  
John Howie ◽  
Steven Duplij ◽  
Ali Mostafazadeh ◽  
Masaki Yasue ◽  
Vladimir Ivashchuk
Keyword(s):  
Banach Algebra ◽  
Infinite Dimensional

scholarly journals On one-sided primitivity of Banach algebras

2010 ◽  
Vol 53 (1) ◽  
pp. 111-123 ◽  
Author(s):  
M. J. Crabb ◽  
J. Duncan ◽  
C. M. McGregor
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Semigroup Algebra ◽  
Alternative Proof ◽  
Infinite Dimensional ◽  
Finite Dimensional

AbstractLet S be the semigroup with identity, generated by x and y, subject to y being invertible and yx = xy2. We study two Banach algebra completions of the semigroup algebra ℂS. Both completions are shown to be left-primitive and have separating families of irreducible infinite-dimensional right modules. As an appendix, we offer an alternative proof that ℂS is left-primitive but not right-primitive. We show further that, in contrast to the completions, every irreducible right module for ℂS is finite dimensional and hence that ℂS has a separating family of such modules.

Relations between the homologies of C*-algebras and their commutative C*-subalgebras

2002 ◽  
Vol 132 (1) ◽  
pp. 155-168
Author(s):  
ZINAIDA A. LYKOVA
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Banach Algebra ◽  
Left Ideal ◽  
Separable Hilbert Space ◽  
Infinite Dimensional ◽  
C Algebras

The paper concerns the identification of projective closed ideals of C*-algebras. We prove that, if a C*-algebra has the property that every closed left ideal is projective, then the same is true for all its commutative C*-subalgebras. Further, we say a Banach algebra A is hereditarily projective if every closed left ideal of A is projective. As a corollary of the stated result we show that no infinite-dimensional AW*-algebra is hereditarily projective. We also prove that, for a commutative C*-algebra A contained in [Bscr ](H), where H is a separable Hilbert space, the following conditions are equivalent: (i) A is separable; and (ii) the C*-tensor product A [otimes ]minA is hereditarily projective. Howerever, there is a non-separable, hereditarily projective, commutative C*-algebra A contained in [Bscr ](H), where H is a separable Hilbert space.

scholarly journals A Note on Finite-Dimensional Differentiable Mappings

1969 ◽  
Vol 9 (3-4) ◽  
pp. 405-408 ◽  
Author(s):  
K. J. Palmer ◽  
Sadayuki Yamamuro
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Continuous Linear ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Image Position ◽  
Differentiable Mappings

Let E be a real infinite-dimensional Banach space. Let ℒ be the Banach algebra of all continuous linear mappings of E into itself with topology defined by the norm:

scholarly journals Topologically irreducible representations of the Banach -algebra associated with a dynamical system

2017 ◽  
Vol 38 (5) ◽  
pp. 1768-1790
Author(s):  
AKI KISHIMOTO ◽  
JUN TOMIYAMA
Keyword(s):  
Dynamical System ◽  
Tensor Product ◽  
Banach Algebra ◽  
Irreducible Representations ◽  
Type I ◽  
Topological Dynamical System ◽  
Infinite Dimensional ◽  
New Class ◽  
Mild Conditions ◽  
Ergodic Measures

We describe (infinite-dimensional) irreducible representations of the crossed product C$^{\ast }$-algebra associated with a topological dynamical system (based on $\mathbb{Z}$) and we show that their restrictions to the underlying $\ell ^{1}$-Banach $\ast$-algebra are not algebraically irreducible under mild conditions on the dynamical system. The above description of irreducible representations has two ingredients, ergodic measures on the space and ergodic extensions for the tensor product with type I factors, the latter of which may not have been explicitly taken up before but which will be explored by means of examples. A new class of ergodic measures is also constructed for irrational rotations on the circle.

scholarly journals Hypercyclictty and Countable Hypercyclicity for Adjoint of Operators

2010 ◽  
Vol 7 (1) ◽  
pp. 191-199
Author(s):  
Baghdad Science Journal
Keyword(s):  
Hilbert Space ◽  
Banach Algebra ◽  
Complex Hilbert Space ◽  
Linear Operators ◽  
Hypercyclic Operator ◽  
Dense Orbit ◽  
Bounded Linear ◽  
Hyperinvariant Subspace ◽  
Infinite Dimensional ◽  
Bounded Set

Let be an infinite dimensional separable complex Hilbert space and let , where is the Banach algebra of all bounded linear operators on . In this paper we prove the following results. If is a operator, then 1. is a hypercyclic operator if and only if D and for every hyperinvariant subspace of . 2. If is a pure, then is a countably hypercyclic operator if and only if and for every hyperinvariant subspace of . 3. has a bounded set with dense orbit if and only if for every hyperinvariant subspace of , .

scholarly journals The weak closure of the set of singular elements in a Banach algebra

1970 ◽  
Vol 2 (1) ◽  
pp. 89-93 ◽  
Author(s):  
J.D. Gray
Keyword(s):  
Banach Algebra ◽  
Weak Topology ◽  
Banach Algebras ◽  
Infinite Dimensional ◽  
Weak Closure

In this note it is proved that for a certain class of infinite dimensional Banach algebras the set of singular elements (the non-units) is dense in the weak topology.

scholarly journals The Fixed Point Property of a Banach Algebra Generated by an Element with Infinite Spectrum

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
P. Thongin ◽  
W. Fupinwong
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Algebra ◽  
Convex Subset ◽  
Fixed Point Property ◽  
Point Property ◽  
Infinite Dimensional ◽  
Complex Banach Algebra

A Banach spaceXis said to have the fixed point property if for each nonexpansive mappingT:E→Eon a bounded closed convex subsetEofXhas a fixed point. LetXbe an infinite dimensional unital Abelian complex Banach algebra satisfying the following: (i) condition (A) in Fupinwong and Dhompongsa, 2010, (ii) ifx,y∈Xis such thatτx≤τy,for eachτ∈Ω(X),thenx≤y,and (iii)inf⁡{r(x):x∈X,x=1}>0.We prove that there exists an elementx0inXsuch that〈x0〉R=∑i=1kαix0i:k∈N,αi∈R¯does not have the fixed point property. Moreover, as a consequence of the proof, we have that, for each elementx0inXwith infinite spectrum andσ(x0)⊂R,the Banach algebra〈x0〉=∑i=1kαix0i:k∈N,αi∈C¯generated byx0does not have the fixed point property.

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