On invariant operator ranges

Nordgren, E.; Radjabalipour, M.; Radjavi, H.; Rosenthal, P.

doi:10.1090/S0002-9947-1979-0531986-6

On invariant operator ranges
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by E. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal PDF

Trans. Amer. Math. Soc. 251 (1979), 389-398 Request permission

Abstract:

A matricial representation is given for the algebra of operators leaving a given dense operator range invariant. It is shown that every operator on an infinite-dimensional Hilbert space has an uncountable family of invariant operator ranges, any two of which intersect only in 0.

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