Completely Continuous Linear Maps on Semigroup Algebras

January 2013
Asian Academy of Management Journal of Accounting & Finance;2013, Vol. 9 Issue 1, p151
Academic Journal
For a locally compact group G, L1(G) is its group algebra and L∞(G) is the dual of L1(G). Crombez and Govaerts introduced the notion of a uniformly measurable function in L∞(G) and proved that such a function induces a completely continuous operator. The aim of this paper is to go further and generalize the above results to foundation semigroup algebras. We study completely continuous linear maps on semigroup algebras which commute with translations.


Related Articles

  • RIESZ-DUNFORD REPRESENTATION THEOREM FOR UNIFORMLY CONTINUOUS SEMIGROUPS. LEMLE, Ludovic Dan; BÎNZAR, Tudor; PATER, Lucian Flavius; BALASOIU, Valentina // Annals of the Faculty of Engineering Hunedoara - International J;Sep2011, Vol. 9 Issue 3, p481 

    This note presents a Riesz-Dunford type representation and a Bromwich type representation for uniformly continuous semigroups on a Banach space.

  • Some properties of b-weakly compact operators on Banach lattice. Na Cheng; Zi-li Chen // International Journal of Information & Mathematical Sciences;Jun2010, Vol. 6 Issue 2, p96 

    We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is...

  • THE WEAKLY COMPACT APPROXIMATION OF THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES. Qingying Bu // Annales Academiae Scientiarum Fennicae. Mathematica;2012, Vol. 37 Issue 2, p461 

    We show that X…Y , the projective tensor product of Banach spaces X and Y , has the (bounded) compact approximation property if and only if both X and Y have the same property. We also show that X…Y has the weakly compact approximation property (W.A.P.) if both X and Y has the W.A.P....

  • Duality Property for Positive Weak Dunford-Pettis Operators. Aqzzouz, Belmesnaoui; Bouras, Khalid; Moussa, Mohammed // International Journal of Mathematics & Mathematical Sciences;2011, p1 

    We prove that an operator is weak Dunford-Pettis if its adjoint is one but the converse is false in general, and we give some necessary and sufficient conditions under which each positive weak Dunford-Pettis operator has an adjoint which is weak Dunford-Pettis.

  • On the dual positive Schur property in Banach lattices. Wnuk, Witold // Positivity;Sep2013, Vol. 17 Issue 3, p759 

    The paper contains several characterizations of Banach lattices $$E$$ with the dual positive Schur property (i.e., $$0 \le f_n \xrightarrow {\sigma (E^*,E)} 0$$ implies $$\Vert f_n\Vert \rightarrow 0$$) and various examples of spaces having this property. We also investigate relationships...

  • Caristi Fixed Point Theorem in Metric Spaces with a Graph. Alfuraidan, M. R.; Khamsi, M. A. // Abstract & Applied Analysis;2014, p1 

    We discuss Caristi's fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi's fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with...

  • Module Amenability for Semigroup Algebras. Amini, Massoud // Semigroup Forum;Sep/Oct2004, Vol. 69 Issue 2, p243 

    We extend the concept of amenability of a Banach algebra A to the case that there is an extra 21-module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A =l� (S) as a Banach module over 21 = l� (E) is module amenable if and only if...

  • SEMIGROUP ALGEBRAS AND THEIR WEAK MODULE AMENABILITY. Bodaghi, Abasalt // Journal of Applied Functional Analysis;Jan2012, Vol. 7 Issue 1/2, p332 

    In the present paper, the weak module amenability for a Banach algebra is investigated and it is proven that for an inverse semigroup S with the set of idempotents E, ℓ¹ (S) is ℓ¹ (E)-weakly module amenable. Also, it is shown that C * (S), the enveloping C * -algebra of...

  • CO-EP BANACH ALGEBRA ELEMENTS. BENÍTEZ, JULIO; BOASSO, ENRICO; RAKOČEVIĆ, VLADIMIR // Banach Journal of Mathematical Analysis;2015, Vol. 9 Issue 1, p27 

    In this work, given a unital Banach algebra A and ɑ ∈ A such that ɑ has a Moore-Penrose inverse ɑ†, it will be characterized when ɑɑ† -- ɑ†ɑ is invertible. A particular subset of this class of objects will also be studied. In addition,...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics