Differential inequalities and divisibility in operator algebras

Generalized additive functional inequalities in Banach algebras

Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

Operator Theory and Operator Algebras

Formal differential operators, vertex operator algebras and zeta–values, I

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of ζ–functions at the negative integers. By using formal calculus techniques we discuss the appearance of values of ζ–functions at the negative integers underlying the construction. In addition we provide a conceptual explanation of this phenomen...

Some weighted operator geometric mean inequalities

In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...

Matrix and Operator Inequalities

In this paper we prove certain inequalities involving matrices and operators on Hilbert spaces. In particular inequalities involving the trace and the determinant of the product of certain positive definite matrices.