Papers by Ali Reza Medghalchi
Glasnik Matematicki, 2018
Exact operator spaces are known to be locally reflexive, but the converse is not true. We introdu... more Exact operator spaces are known to be locally reflexive, but the converse is not true. We introduce the notion of global exactness and show that it is equivalent to reflexivity for injective operator spaces.
Bulletin of the Korean Mathematical Society, 2016
In this paper we extend Takahashi's fixed point theorem on discrete semigroups to general semi-to... more In this paper we extend Takahashi's fixed point theorem on discrete semigroups to general semi-topological semigroups. Next we define the semi-asymptotic non-expansive action of semi-topological semigroups to give a partial affirmative answer to an open problem raised by A.T-M. Lau.
Czechoslovak Mathematical Journal, 2005
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Bolema: Boletim de Educação Matemática, 2013
Proceedings Mathematical Sciences, 2005
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force... more The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group G, G is compact if there exists a measure µ in Soc(L 1 (G)) such that µ(G) = 0. We also prove that G is finite if Soc(M(G)) is closed and every nonzero left ideal in M(G) contains a minimal left ideal.
Rocky Mountain Journal of Mathematics, 2011
ABSTRACT The first cohomology group of a Banach algebra A with coefficients in a Banach A-bimodul... more ABSTRACT The first cohomology group of a Banach algebra A with coefficients in a Banach A-bimodule X, denoted by H 1 (A,X), is the quotient space of the space of all continuous derivations from A to X modulo the space of inner derivations. An algebra A is called n-weakly amenable if H 1 (A,A (n) )={0}, where A (n) is the nth conjugate space (module) of A. It is often important to calculate the first cohomology group for different types of Banach algebras; for example, B. E. Forrest and L. W. Marcoux [Trans. Am. Math. Soc. 354, No. 4, 1435–1452 (2002; Zbl 1014.46017)] and [Indiana Univ. Math. J. 45, No. 2, 441–462 (1996; Zbl 0890.46035)] have determined the first cohomology group of a class of Banach algebras which they called triangular Banach algebras. Also, Y. Zhang [Trans. Am. Math. Soc. 354, No. 10, 4131–4151 (2002; Zbl 1008.46019)] has proved several general results on the n-weak amenability of module extension Banach algebras. Note that module extension Banach algebras are generalized forms of triangular Banach algebras. Based upon ideas from [Zbl 0890.46035], the authors of the paper under review compute the first cohomology group H 1 (A⊕X,A⊕X) for the module extension Banach algebra A⊕X. In particular, they calculate the first cohomology group H 1 (A⊕X,Y) for an A-bimodule Y which is an A⊕X-bimodule in a canonical fashion. Finally, the authors illustrate the scope of their results by some interesting examples yielding some non-n-weakly amenable Banach algebras.
Mathematische Zeitschrift, 1992
Journal of the London Mathematical Society, 1993
We investigate the algebraic structure of the spectrum Cl of U°(G) for a locally compact group G.... more We investigate the algebraic structure of the spectrum Cl of U°(G) for a locally compact group G. In contrast to the compact and discrete cases, when G has neither of these properties, h is never a semigroup. For <7-compact G we determine exactly when the product of two elements of Q. is in Q, but we present an example which suggests that for general groups the underlying set theory may have an effect. Our principal tool, which has independent interest, is a topological structure theorem for the JSf^-compactification of an arbitrary locally compact group.
Banach J Math Anal, 2009
Let A be a Banach algebra and let ϕ and ψ be continuous homomorphisms on A. We consider the follo... more Let A be a Banach algebra and let ϕ and ψ be continuous homomorphisms on A. We consider the following module actions on A,
Indagationes Mathematicae, 2005
We study here the simple infinite-dimensional quotients of the group C*-algebras of two discrete ... more We study here the simple infinite-dimensional quotients of the group C*-algebras of two discrete 6-dimensional nilpotent groups H6,] and H6,2 as the higher-dimensional analogues of the irrational rotation algebras. R Milnes and S. Walters, jointly and individually, have studied the lower-dimensional cases in a series of papers, and also have started the study of some other 6-dimensional groups. For G = H6,1 or H6,2, we can determine the crossed product presentations for the simple quotients of C*(G), and matrix representations for those arising from non-faithful representations of the groups. The isomorphism classifications of these quotients are obtained using K-theoretic tools, namely, the K-groups and the range of trace on K0. This marks the first use of K-theory in the classification of quotients for 6-dimensional groups.
We show that an infinite dimensional injective operator space V has an infinite dimensional opera... more We show that an infinite dimensional injective operator space V has an infinite dimensional operator subspace, completely isometric to the row or column Hilbert spaces or l∞. When the third case does not happen, we characterize V as a finite direct sum of bounded operators B(H, K) with H or K finite dimensional. We characterize injective operator spaces V and W for which the spacial (injective) tensor product V⊗ˇW is injective. We give a similar characterization for injectivity of the Haagerup tensor product of injective operator spaces.
Acta Mathematica Vietnamica
Publicationes Mathematicae Debrecen, 2013
ABSTRACT Let $V ∼= B(K,H)$ where $H$ and $K$ are Hilbert spaces. Then we know that $I_{11}(V ) ∼=... more ABSTRACT Let $V ∼= B(K,H)$ where $H$ and $K$ are Hilbert spaces. Then we know that $I_{11}(V ) ∼= B(H)$. By using this, our aim is to characterize injective operator space $V$ for which $I_{11}(V )∼= B(H)$. We have shown that this is the case if and only if $V ∼= B(K,H)$ where $K$ is a Hilbert space.
Mathematische Nachrichten, 2014
ABSTRACT We show that for a compact hypergroup K, the hypergroup algebra is amenable as a Banach ... more ABSTRACT We show that for a compact hypergroup K, the hypergroup algebra is amenable as a Banach algebra if the set of hyperdimensions of irreducible representations of K is bounded above. Conversely if is amenable, the set of ratios of the hyperdimension to the dimension of irreducible representations of K is bounded above. These are equivalent for compact commutative hypergroups.
IRANIAN JOURNAL OF MATHEMATICAL …, 2006
6 : IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI) NOVEMBER 2006; 1(2):1-8. SPE... more 6 : IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI) NOVEMBER 2006; 1(2):1-8. SPECTRUM OF THE FOURIER-STIELTJES ALGEBRA OF A SEMIGROUP AMINI MASOUD,MEDGHALCHI AAR ...
Publicationes mathematicae Debrecen, 2013
Glasnik Matematicki, 2013
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Papers by Ali Reza Medghalchi