CONTENTS 1. Introduction...................................................................................................5 2. N-tuples of linear transformations in finite-dimensional space......................8 3. Toeplitz operators on the polydisc and the unit ball....................................18 4. Subspaces of weighted shifts.....................................................................23 5. Joint spectra for N-tuples of operators........................................................27 6. Algebras of operator weighted shifts...........................................................30 7. Functional calculus for N-tuples of contractions..........................................37 8. Dual algebras, invariant subspace problem and reflexivity..........................44 9. Reflexivity of jointly quasinormal operators and spherical isometries..........45 10. Reflexivity and existence of invariant subspaces......................................47 11. Questions and open problems..................................................................56 References.....................................................................................................58
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