Contractive maps on operator ideals and norm inequalities II

Operator-valued extensions of matrix-norm inequalities

The bilinear inequality is derived from the linear one with the help of an operatorvalued version of the Cauchy-Schwarz inequality. All these results, at least in their finite form, are obtained by simple and elegant methods well within the scope of a basic course on Hilbert spaces. (They can alternatively be obtained by tensor product techniques, but in the author’s view, these methods are les...

Norm Comparison Inequalities for the Composite Operator

The purpose of this paper is to establish the Lipschitz norm and BMO norm inequalities for the composition of the homotopy operator T and the projection operator H applied to differential forms in R, n ≥ 2. The harmonic projection operator H, one of the key operators in the harmonic analysis, plays an important role in the Hodge decomposition theory of differential forms. In the meanwhile, the ...

Some results on weakly contractive maps

In this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. Some of these results are improved by using different arguments of control functions. Examples are presented showing that some generalizations cannot be obtained and also that our results are distinct from the existing ones.

On topological transitive maps on operator algebras

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Multiplicative bijective maps on standard operator algebras