K-QUASI CLASS Q AND k-QUASI * CLASS Q COMPOSITION OPERATORS ON WEIGHTED HARDY SPACE

PROPERTY (ω) AND QUASI-CLASS (A,k) OPERATORS

In this paper, we prove the following assertions: (i) If T is of quasiclass (A, k), then T is polaroid and reguloid; (ii) If T or T ∗ is an algebraically of quasi-class (A, k) operator, then Weyls theorem holds for f(T ) for every f ∈ Hol(σ(T )); (iii) If T ∗ is an algebraically of quasi-class (A, k) operator, then a-Weyls theorem holds for f(T ) for every f ∈ Hol(σ(T )); (iv) If T ∗ is algebra...

THE FUGLEDE–PUTNAM THEOREM AND PUTNAM’S INEQUALITY FOR QUASI-CLASS (A, k) OPERATORS

An operator T ∈ B(H) is called quasi-class (A, k) if T ∗k(|T | − |T |)T k ≥ 0 for a positive integer k, which is a common generalization of class A. The famous Fuglede–Putnam’s theorem is as follows: the operator equation AX = XB implies A∗X = XB∗ when A and B are normal operators. In this paper, firstly we show that if X is a Hilbert-Schmidt operator, A is a quasi-class (A, k) operator and B∗ ...

Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...

Generalized composition operators on weighted Hardy spaces

QUASI-∗ STRUCTURE ON q-POINCARE ALGEBRAS

We use braided groups to introduce a theory of ∗-structures on general inhomogeneous quantum groups, which we formulate as quasi-∗ Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix form appro...