• A NOTE ON INVARIANT SUBSPACES OF SOME OPERATORS IN HILBERT SPACE

IRENE M. MUTETI*, BERNARD M. NZIMBI, STANLEY K. IMAGIRI, JAIRUS M. KHALAGAI

Abstract


In this paper, we show that if  is a nontrivial invariant for both and , then M is invariant or  invariant. An example is provided to illustrate that if  is invariant, then it is not necessarily invariant for either and . However if  and  have same structure and  is invariant for  then it is also invariant for and .


Keywords


Invariant subspaces, Nilpotent operators.

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