Operators invariant relative to a completely nonunitary contraction

Relative Number of Non-Invariant Operators in a Group.

Completely Continuous Composition Operators

A composition operator Tbf = f o b is completely continuous on H1 if and only if \b\ < 1 a.e. If the adjoint operator Tg is completely continuous on VMOA , then 7¿ is completely continuous on Hl . Examples are given to show that the converse fails in general. Two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of ce...

Completely Inversible Operators.

where W is a given distribution of compact carrier. In a previous note' we showed that if W is a punctual distribution (i.e., if eq. (1) is a partial differential-difference equation with constant coefficients), then for every distribution T we can find a distribution S such that equation (1) is satisfied. In this paper we shall characterize completely all distributions W of compact carrier suc...

Unitarity Restoration for the Product of Nonunitary Operators

A proof is given that the polar decomposition procedure for unitarity restoration works for products of invertible nonunitary operators. A brief discussion follows that the unitarity restoration procedure, applied to propagators in spacetimes containing closed timelike curves, is analogous to the original introduction by Feynman of ghosts to restore unitarity in non-abelian gauge theories. (The...

Universal Non-completely-continuous Operators

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into `∞ defined by T0(f) = Z rnf dμ n≥0 , where rn is the nth Rademacher function. It is...