Algebraic Elements and Invariant Subspaces
Yun-Su Kim
TL;DR
This paper proves that certain algebraic elements in non-unitary contractions imply the existence of non-trivial invariant subspaces, advancing understanding in operator theory.
Contribution
It establishes a new link between algebraic elements and invariant subspaces for completely non-unitary contractions.
Findings
Presence of algebraic elements guarantees invariant subspaces.
Provides conditions under which invariant subspaces exist.
Enhances theoretical understanding of operator structure.
Abstract
We prove that if a completely non-unitary contraction T in L(H) has a non-trivial algebraic element h, then T has a non-trivial invariant subspace.
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Taxonomy
TopicsMatrix Theory and Algorithms · Polynomial and algebraic computation · Advanced Theoretical and Applied Studies in Material Sciences and Geometry