scholarly journals A Banach algebra which is generated by idempotents

2015 ◽  
Vol 24 (1) ◽  
pp. 97-99
Author(s):  
A. ZIVARI-KAZEMPOUR ◽  
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Locally Compact ◽  
Locally Compact Hausdorff Space ◽  
Totally Disconnected

In this paper we show that the Banach algebra C0(X), where X is a locally compact Hausdorff space, is generated by idempotents if and only if X is totally disconnected.

scholarly journals OPERATORS ON BANACH ALGEBRA VALUED FUNCTION SPACES

1992 ◽  
Vol 23 (3) ◽  
pp. 233-238
Author(s):  
JOR-TING CHAN
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Function Spaces ◽  
Linear Operators ◽  
Locally Compact ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Locally Compact Hausdorff Space

Let $S$ be a locally compact Hausdorff space and let $A$ be a Banach algebra. Denote by $C_0(S, A)$ the Banach algebra of all $A$-valued continuous functions vanishing at infinity on $S$. Properties of bounded linear operators on $C_0(S,A)$, like multiplicativity, are characterized by Choy in terms of their representing measures. We study these theorems and give sharper results in certain cases.

scholarly journals Spatial numerical ranges of elements of subalgebras ofC0(X)

2000 ◽  
Vol 23 (12) ◽  
pp. 827-831
Author(s):  
Sin-Ei Takahasi
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Numerical Range ◽  
Commutative Banach Algebra ◽  
Locally Compact ◽  
Continuous Complex ◽  
Complex Valued ◽  
Locally Compact Hausdorff Space

WhenAis a subalgebra of the commutative Banach algebraC0(X)of all continuous complex-valued functions on a locally compact Hausdorff spaceX, the spatial numerical range of element ofAcan be described in terms of positive measures.

scholarly journals On the theorem of Kishi for a continuous function-kernel

1974 ◽  
Vol 53 ◽  
pp. 127-135 ◽  
Author(s):  
Isao Higuchi ◽  
Masayuki Itô
Keyword(s):  
Continuous Function ◽  
Potential Theory ◽  
Compact Hausdorff Space ◽  
Symmetric Function ◽  
Hausdorff Space ◽  
Locally Compact ◽  
Continuity Principle ◽  
Lower Semi ◽  
Locally Compact Hausdorff Space

In the potential theory with respect to a non-symmetric function-kernel, the following theorem is obtained by M. Kishi ([3]).Let X be a locally compact Hausdorff space and G be a lower semi-continuous function-kernel on X. Assume that G(x, x)>0 for any x in X and that G and the adjoint kernel Ğ of G satisfy “the continuity principle”.

scholarly journals On projective lift and orbit spaces

1994 ◽  
Vol 50 (3) ◽  
pp. 445-449 ◽  
Author(s):  
T.K. Das
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Covariant Functor ◽  
Hausdorff Spaces ◽  
Orbit Spaces ◽  
Locally Compact ◽  
Discontinuous Group ◽  
Coreflective Subcategory ◽  
Group Of Homeomorphisms ◽  
Locally Compact Hausdorff Space

By constructing the projective lift of a dp-epimorphism, we find a covariant functor E from the category Cd of regular Hausdorff spaces and continuous dp-epimorphisms to its coreflective subcategory εd consisting of projective objects of Cd We use E to show that E(X/G) is homeomorphic to EX/G whenever G is a properly discontinuous group of homeomorphisms of a locally compact Hausdorff space X and X/G is an object of Cd.

scholarly journals Multipliers of Modules of Continuous Vector-Valued Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Normed Spaces ◽  
Locally Compact ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space ◽  
Locally Convex

In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

scholarly journals A Riemann integral in a locally compact Hausdorff space

1986 ◽  
Vol 41 (1) ◽  
pp. 115-137 ◽  
Author(s):  
S. I. Ahmed ◽  
W. F. Pfeffer
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Sufficient Condition ◽  
Lebesgue Integral ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Riemann Integral ◽  
Variational Integrals ◽  
Necessary And Sufficient ◽  
Locally Compact Hausdorff Space

AbstractWe present a systematic and self-contained exposition of the generalized Riemann integral in a locally compact Hausdorff space, and we show that it is equivalent to the Perron and variational integrals. We also give a necessary and sufficient condition for its equivalence to the Lebesgue integral with respect to a suitably chosen measure.

scholarly journals On dimension andweight of a local contact algebra

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5481-5500
Author(s):  
G. Dimov ◽  
E. Ivanova-Dimova ◽  
I. Düntsch
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Local Contact ◽  
Continuous Maps ◽  
Contact Algebra ◽  
Contact Algebras ◽  
Locally Compact Hausdorff Space

As proved in [16], there exists a duality ?t between the category HLC of locally compact Hausdorff spaces and continuous maps, and the category DHLC of complete local contact algebras and appropriate morphisms between them. In this paper, we introduce the notions of weight wa and of dimension dima of a local contact algebra, and we prove that if X is a locally compact Hausdorff space then w(X) = wa(?t(X)), and if, in addition, X is normal, then dim(X) = dima(?t(X)).

The Primitive Ideal Space of a C*-Algebra

1974 ◽  
Vol 26 (1) ◽  
pp. 42-49 ◽  
Author(s):  
John Dauns
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Complete Characterization ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Compact Sets ◽  
Locally Compact ◽  
C Algebra ◽  
Weak Star ◽  
Locally Compact Hausdorff Space

The commutative Gelfand-Naimark Theorem says that any commutative C*-algebra A is isomorphic to the ring C0(M, C) of all continuous complex-valued functions tending to zero outside of compact sets of a locally compact Hausdorff space M. A very important part of this theorem is an intrinsic and also a complete characterization of M as exactly the primitive ideal space of A in the hull-kernel (or weak-star) topology. In the non-commutative case, A ≌ Γ0(M, E)—the ring of sections tending to zero outside of compact subsets of a locally compact Hausdorff space M with values in the stalks or fibers E.

scholarly journals Distinguishedness of weighted Fréchet spaces of continuous functions

1992 ◽  
Vol 35 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Françoise Bastin
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Fréchet Space ◽  
Frechet Space ◽  
Fréchet Spaces ◽  
Density Condition ◽  
Locally Compact ◽  
Spaces Of Continuous Functions ◽  
Locally Compact Hausdorff Space

In this paper, we prove that if is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that then the Fréchet space C(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequence satisfies condition (H) (cf. e.g.‵[1] for the introduction of (H)). As a consequence, the bidual λ∞(A) of the distinguished Köthe echelon space λ0(A) is distinguished if and only if the space λ1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Köthe echelon spaces.

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