In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group:...

The largest class of algebraic hyper structures satisfying the module like axioms is the v H module. In this paper, we consider the category of v H -modules and prove that the direct limit always exists in this category. Direct limits are defined by a universal property, and so are unique. The most powerful tool in order to obtain a module from a given v H module is the quotient out procedure. ...

Let G be a connected reductive algebraic group defined over an algebraically closed field of characteristic p > 0. Our first aim in this note is to give concise and uniform proofs for two fundamental and deep results in the context of Serre’s notion of G-complete reducibility, at the cost of less favourable bounds. Here are some special cases of these results: Suppose that the index (H : H◦) is...

In this paper we study G-extensions of real and complex representations of a closed normal subgroup H of a compact Lie group G when G/H is connected. The main result gives a necessary and sufficient condition for every complex irreducible H-module to extend to a G-module. In particular, we show that every complex Hmodule extends to a G-module if the fundamental group of G/H is torsion free. We ...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

Let G be a finite group and k a fixed algebraically closed field of characteristic p>0 . If p is odd, let H(; be the subring of H*(G,k) consisting of elements of even degree; following [20-22] we take H~=H*(G,k) if p=2, though one could just as well use the subring of elements of even degree for all p. H a is a finitely generated commutative k-algebra [13], and we let Va denote its associated a...