On semi-inner product algebras

$C^{*}$-semi-inner product spaces

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS

The Lanczos Method with Semi-inner Product

The spectral transformation Lanczos method is very popular for solving large scale Her-mitian generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-inner product must be used. This may lead to instabilities and breakdown. In this paper, we suggest a cure for breakdown by use of an implicit restart in the Lanc...

On (Semi)Topological $BL$-algebras

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

X-inner Automorphisms of Semi-commutative Quantum Algebras

Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantummatrices, q-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras U(L+) of even Lie color algebras are also semi-commutative. In this paper, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras. The t...