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By Peter G. Casazza

This monograph offers a constitution concept for the more and more vital Banach house came across through B.S. Tsirelson. the elemental development might be obtainable to graduate scholars of practical research with an information of the speculation of Schauder bases, whereas issues of a extra complex nature are awarded for the expert. Bounded linear operators are studied by utilizing finite-dimensional decompositions, and complemented subspaces are studied at size. A myriad of variation buildings are awarded and explored, whereas open questions are broached in virtually each bankruptcy. appendices are hooked up: one facing a working laptop or computer application which computes norms of finitely-supported vectors, whereas the opposite surveys fresh paintings on vulnerable Hilbert areas (where a Tsirelson-type house presents an example).

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2 Minimal realizations in non-commutative de Branges–Rovnyak spaces . . . . . . . . . . . . . . . . . . . 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Matrix-J-unitary Rational Formal Power Series 51 1. Introduction In the present paper we study a non-commutative analogue of rational matrixvalued functions which are J-unitary on the imaginary line or on the unit circle and, as a special case, J-inner ones.

PhD thesis, The Weizmann Institute of Sciences, 1986. G. Kre˘n. ˘ Continuous analogues of propositions for polynomials orthogonal on the unit circle. Dokl. Akad. Nauk. SSSR, 105:637–640, 1955. G. Kre˘n. Topics in differential and integral equations and operator theory, volume 7 of Operator theory: Advances and Applications. Birkhauser ¨ Verlag, Basel, 1983. Edited by I. Gohberg, Translated from the Russian by A. Iacob. G. Kre˘n ˘ and H. Langer. Uber die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume Πk .

1 Minimal Givone–Roesser realizations and the Stein equation . . . 2 The associated structured Hermitian matrix . . . . . . . . . . . 3 Minimal matrix-J-unitary factorizations . . . . . . . . . . . . . 4 Matrix-unitary rational formal power series . . . . . . . . . . . . 85 6 Matrix-J-inner rational formal power series . . . . . . . . . . . . . . 1 A multivariable non-commutative analogue of the half-plane case . . . . . . . .

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