The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operatorvalued free probability. The paper presents constructions for maps with similar properties to the H and K transforms from the literature, semi inner-product bimodule analogues for the monotone and weakly monotone product of Hilbert spaces, an ad-hoc versio...

We show that the Green correspondence induces an injective group homomorphism from linear source Picard L(B) of a block B finite algebra to L(C), where C is Brauer correspondent B. This maps trivial T(B) T(C). further endopermutation E(B) bounded in terms defect groups and when has normal E(B)=L(B). Finally we prove rank any invertible B-bimodule by

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 extended Cuntz–Pimsner algebra E(H), introduced by Pimsner, is constructed from a Hilbert B, B–bimodule H over a C∗–algebra B. In this paper we investigate the Haagerup invariant Λ(·) for these algebras, the main result being that Λ(E(H)) = Λ(B) when H is full over B. In particular, E(H) has the completely bounded approximation property if and only if the same is true for B.

For an extension of associative algebras B ⊂ A over a field and A-bimodule X, we obtain Jacobi–Zariski long nearly exact sequence relating the Hochschild homologies B, relative homology, all them with coefficients in X. This is twice three. There spectral which converges to gap exactness.

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH(B) with coefficients in the B–B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by E = ExtC(DC,C), then we prove that HH (B) is isomorphic, as a vector space, to the direct sum of HH(C) with HH(B,E). This yields homological interpretations for results of the first and the fourth au...

Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S :AMNE is intertwining if the bilinear map (a, b)PN (δ"S ) (a, b)B a[Sb®S(ab)­Sa[b, A¬AMNE, is continuous, and a linear map D :AMNE is a deriŠation if δ"D ̄ 0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous. The purpose of the present paper is to prove that the continui...