Composition Operators with Universal Translates on S2(D)

It is known that the Invariant Subspace Problem for Hilbert spaces is equivalent to the statement that all minimal non-trivial invariant subspaces for a universal operator are one dimensional.In this paper, we characterize all linear fractional composition operators and their adjoints that have universal translates on the spaceS2(D). Moreover, we characterize all adjoints of linear fractional composition operators that have universal translates on the Hardy space H-2(D). In addition, we consider the minimal invariant subspaces of the composition operatorC phi aonS(2)(D), where phi a(z)=az+1-a,a is an element of(0,1). Finally, some relationships between complex symmetry and universality for bounded linear operators and commuting pairs of operators on a complex separable, infinite dimensional Hilbert space are explored

Automated summary

This paper investigates the Invariant Subspace Problem for Hilbert spaces, characterizing linear fractional composition operators and their adjoints with universal translates on the spaces S2(D) and H-2(D). It also explores the relationships between complex symmetry and universality for bounded linear operators and commuting pairs of operators on a complex separable, infinite dimensional Hilbert space.