Constructing an operator from a complete and minimal set

Author： Nath Jiban  

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.133, Iss.3, 2003-06, pp. : 653-663

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Abstract

Let {ei}i=1∞ be a complete and minimal set in a Hilbert space X, which is not an unconditional basis. Then there exists an operator that is densely defined on X, does not have a good spectral behaviour and all the vectors {ei} are its eigenvectors.

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