in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

this paper is concerned with the best proximity pair problem in hilbert spaces. given two subsets $a$ and $b$ of a hilbert space $h$ and the set-valued maps $f:a o 2^ b$ and $g:a_0 o 2^{a_0}$, where $a_0={xin a: |x-y|=d(a,b)~~~mbox{for some}~~~ yin b}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in a$ such that $$d(g(x_0),f(x_0))=d(a,b).$$

Suppose that A and B are unital Banach algebras with units 1A and 1B , respectively, M is a unital Banach A−B-bimodule, T =   A M 0 B   is the triangular Banach algebra, X is a unital T -bimodule, XAA = 1AX1A, XBB = 1BX1B , XAB = 1AX1B and XBA = 1BX1A. Applying two nice long exact sequences related to A, B, T , X, XAA, XBB , XAB and XBA we establish some results on (co)homology of triangu...

It is well-known that if T is a Dm–Dn bimodule map on the m×n complex matrices, then T is a Schur multiplier and ‖T‖cb = ‖T‖. If n = 2 and T is merely assumed to be a right D2-module map, then we show that ‖T‖cb = ‖T‖. However, this property fails if m ≥ 2 and n ≥ 3. For m ≥ 2 and n = 3, 4 or n ≥ m2 we give examples of maps T attaining the supremum C(m,n) = sup{‖T‖cb : T a right Dn-module map o...

We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}...

Let δ be a nondegenerate coaction of G on a C∗-algebra B, and let H be a closed subgroup of G. The dual action δ̂ : H → Aut(B×δ G) is proper and saturated in the sense of Rieffel, and the generalised fixed-point algebra is the crossed product of B by the homogeneous space G/H . The resulting Morita equivalence is a version of Mansfield’s imprimitivity theorem which requires neither amenability n...

We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference case is interpretation value map, classically element group. interpretations as states algebra, elements a Hilbert $C^{*} $-bimodule $\frac{1}{2}$ densities and dual algebra. examples complex valued functions $S_{3}$ $\mathbb{Z}$, Woronowicz's matrix quantum ...

The connection between doubly transitive permutation groups G on a finite set Cl which are not doubly primitive and automorphism groups of block designs in which X = 1 has been investigated by Sims [2] and Atkinson [1]. If, for a e Q, Ga has a set of imprimitivity of size 2 then it is easy to show that G is either sharply doubly transitive or is a group of automorphisms of a non-trivial block d...

In this paper we effect a systematic study of transitive subgroups of M24, obtaining 5 transitive maximal subgroups of M24 of which one is primitive and four imprimitive. These results, along with the results of the paper, On subgroups of M2i. I, enable us to enumerate all the maximal subgroups of M24. There are, up to conjugacy, nine of them. The complete list includes one more in addition to ...

Let U be a (B, A)-bimodule, A and B rings, formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using left global dimensions B, estimate dimension T-module.