Abstract
LetT be a contraction acting in a separable Hilbert space\(\mathcal{H}\) and leaving invariant a nest\(\mathcal{N}\) of subspaces of\(\mathcal{H}\). We answer the question: when doesT have an isometric extension to\(\mathcal{H}\) ⊕\(\mathcal{H}\) which leaves invariant the nest\(\mathcal{N}\) ⊕\(\mathcal{N}\) = {N ⊕N :N ∈\(\mathcal{N}\);}.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Arveson, Interpolation problems in nest algebras, J. Funct. Anal.20, 208–233 (1975).
A. Feintuch, A. Markus, The lossless embedding problem for time-varying contractive systems, Systems and Control Letters (accepted).
P. Halmos, A Hilbert Space Problem Book, Van Nostrand, 1967.
K. Davidson, Nest Algebras, Pitman Research Notes in Mathematics 191, Longman Scientific & Technical, 1988.
R. Saeks, Synthesis of general linear networks, SIAM J. Appl. Math16, 924–930 (1968).
A. van der Veen, P. Dewilde, Embedding of time-varying contractive systems in lossless realizations, Math. Control Signals Systems7, 306–330 (1994).