Invariant subspace problem for classical spaces of functions
نویسندگان
چکیده
منابع مشابه
The Invariant Subspace Problem
Notes for my lectures in the PSU Analysis Seminar during the winter and spring terms 2013-14, with special emphasis on the 1972 results of Victor Lomonosov.
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The notion of an invariant subspace is fundamental to the subject of operator theory. Given a linear operator T on a Banach space X, a closed subspace M of X is said to be a non-trivial invariant subspace for T if T (M) ⊆M and M 6= {0}, X. This generalizes the idea of eigenspaces of n×n matrices. A famous unsolved problem, called the “invariant subspace problem,” asks whether every bounded line...
متن کاملThe Invariant Subspace Problem
Heeft elke begrensde lineaire operator, werkend op een Hilbert ruimte, een niet-triviale invariante deelruimte? Het antwoord is positief voor zowel eindig-dimensionale ruimtes als voor niet-separabele ruimtes. Het onopgeloste probleem voor het geval daar tussenin, dus voor separabele Hilbert ruimtes staat bekend als het invariante deelruimte probleem. Professor B.S. Yadav van de Indian Society ...
متن کاملSufficient Conditions for the Invariant Subspace Problem
In this note, we provide a few sufficient conditions for the invariant subspace problem. Introduction An important open problem in operator theory is the invariant subspace problem. Since the problem is solved for all finite dimensional complex vector spaces of dimension at least 2, H denotes a separable Hilbert space whose dimension is infinite. It is enough to think for a contraction T , that...
متن کاملMeasurable Choice and the Invariant Subspace Problem
In [1], J. Dyer, A. Pedersen and P. Porcelli announced that an affirmative answer to the invariant subspace problem would imply that every reductive operator is normal. Their argument, outlined in [1], provides a striking application of direct integral theory. Moreover, this method leads to a general decomposition theory for reductive algebras which in turn illuminates the close relationship be...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2011.11.003