S J Bhatt
Articles written in Proceedings – Mathematical Sciences
Volume 105 Issue 4 November 1995 pp 405-409
Uniqueness of the uniform norm and adjoining identity in Banach algebras
Let
Volume 108 Issue 3 October 1998 pp 283-303
A completely positive operator valued linear map ϕ on a (not necessarily unital) Banach *-algebra with continuous involution admits minimal Stinespring dilation iff for some scalar
Volume 111 Issue 1 February 2001 pp 65-94
Topological *-algebras with
Universal
Volume 113 Issue 2 May 2003 pp 179-182
Let
Volume 115 Issue 4 November 2005 pp 437-444
A note on generalized characters
For a compactly generated LCA group G, it is shown that the set
Volume 118 Issue 3 August 2008 pp 425-441
Limit Algebras of Differential Forms in Non-Commutative Geometry
Given a C∗-normed algebra A which is either a Banach ∗-algebra or a Frechet ∗-algebra, we study the algebras ∞A and A obtained by taking respectively the projective limit and the inductive limit of Banach ∗-algebras obtained by completing the universal graded differential algebra ∗A of abstract non-commutative differential forms over A. Various quantized integrals on ∞A induced by a K-cycle on A are considered. The GNS-representation of ∞A defined by a d-dimensional non-commutative volume integral on a d+-summable K-cycle on A is realized as the representation induced by the left action of A on ∗A. This supplements the representation A on the space of forms discussed by Connes (Ch. VI.1, Prop. 5, p. 550 of [C]).
Volume 121 Issue 4 November 2011 pp 417-433
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
S J Bhatt P A Dabhi H V Dedania
Given a weighted discrete abelian semigroup $(S,\omega)$, the semigroup $M_\omega(S)$ of 𝜔-bounded multipliers as well as the Rees quotient $M_\omega(S)/S$ together with their respective weights $\overline{\omega}$ and $\overline{\omega}_q$ induced by 𝜔 are studied; for a large class of weights 𝜔, the quotient $\ell^1(M_\omega(S),\overline{\omega})/\ell^1(S,\omega)$ is realized as a Beurling algebra on the quotient semigroup $M_\omega(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
Volume 132, 2022
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