Open AccessConvergence properties of minimal vectors for normal operators and weighted shifts
Author(s) -
Isabelle Chalendar,
Jonathan R. Partington
Publication year - 2004
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-04-07595-1
Subject(s) - linear subspace , convergence (economics) , annotation , algorithm , sequence (biology) , semantics (computer science) , computer science , mathematics , algebra over a field , pure mathematics , artificial intelligence , programming language , chemistry , biochemistry , economics , economic growth
We study the behaviour of the sequence of minimal vectors corresponding to certain classes of operators on reflexive L p L^p spaces, including multiplication operators and bilateral weighted shifts. The results proved are based on explicit formulae for the minimal vectors, and provide extensions of results due to Ansari and Enflo, and also Wiesner. In many cases the convergence of sequences associated with the minimal vectors leads to the construction of hyperinvariant subspaces for cyclic operators.