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 characte...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 space S^(2)(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 operator Cφa on S^(2)(D),where φa(z)=az+1-a,a ∈(O,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.展开更多
基金K.Han is supported by the National Natural Science Foundation of China(Grant No.12101179)Natural Science Foundation of Hebei Province of China(Grant No.A2022207001)Y.Tang is supported by the National Natural Science Foundation of China(Grant No.12101185)。
文摘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 space S^(2)(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 operator Cφa on S^(2)(D),where φa(z)=az+1-a,a ∈(O,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.
