Abstract
Recent results concerning the existence of a common nontrivial invariant subspace and reflexivity for families of commuting linear bounded Hilbert space operators will be presented; starting with the families of linear transformations on finite dimensional space, through families of isometries, jointly quasinormal operators and spherical isometries, finishing with N-tuples of contractions with dominating spectra. This paper is based On the notes for the series of lectures given in the Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Republic of China in November and December of 1995.
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