REMARKS ABOUT THE INVARIAN SUBSPACE PROBLEM / CONSIDERAÇÕES SOBRE O PROBLEMA DO SUBESPAÇO INVARIANTE

AUTOR(ES)
DATA DE PUBLICAÇÃO

2011

RESUMO

The Invariant Subspace Problem is the most important open question in Operator Theory. Although, there are many partial results, the question remains open for operators on complex, infinite-dimensional, separable Hilbert spaces. To prove that every operator has a non-trivial invariant subspace might be the beginning of a general structure theory for Hilbert space operators. On the other hand, a counterexample would may yield a number of approximation theorems. In this work we present a survey the Invariant Subspace Problem, and in addition we show also how it might be the spectrum of a hyponormal operator (on a complex separable infinitedimensional Hilbert space) which had no nontrivial invariant subspace.

ASSUNTO(S)

subespacos invariantes invariant subspaces operadores hiponormais hiponormal operators espectro spectrum funcao function

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