2009•arXiv (Cornell University)Open access

Every transcendental operator has a non-trivial invariant subspace

Yun-Su Kim

Abstract

In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely non-unitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary contractions without a non-trivial algebraic element, or (Case 3) contractions which are not completely non-unitary. We know that every operator of (Case 3) has a non-trivial invariant subspace. In this paper, we answer to the invariant subspace problem for the operators of (Case 2). Since (Case 1) is simpler than (Case 2), we leave as a question.

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Key concepts: Transcendental number, Invariant subspace problem, Invariant subspace, Subspace topology, Invariant (physics), Reflexive operator algebra, Mathematics, Operator (biology)