caa a22 4500 46793181X CHVBK 20180406152945.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s00020-006-1422-8 doi (NATIONALLICENCE)springer-10.1007/s00020-006-1422-8 Yang Rongwei Department of Mathematics and Statistics, SUNY at Albany, 12222, Albany, NY, U.S.A aut On Two Variable Jordan Block (II) [Elektronische Daten] [Rongwei Yang] Abstract.: On the Hardy space over the bidisk H2(D2), the Toeplitz operators $$T_{{z_{1} }}$$ and $$T_{{z_{2} }} $$ are unilateral shifts of infinite multiplicity. A closed subspace M is called a submodule if it is invariant for both $$T_{{z_{1} }} $$ and $$T_{{z_{2} }} $$ . The two variable Jordan block (S1, S2) is the compression of the pair $$T_{{z_{1} }}, T_{{z_{2} }}$$ to the quotient H2(D2) ⊖M. This paper defines and studies its defect operators. A number of examples are given, and the Hilbert-Schmidtness is proved with good generality. Applications include an extension of a Douglas-Foias uniqueness theorem to general domains, and a study of the essential Taylor spectrum of the pair (S1, S2). The paper also estabishes a clean numerical estimate for the commutator [S1*, S2] by some spectral data of S1 or S2. The newly-discovered core operator plays a key role in this study. Birkhäuser Verlag, Basel, 2006 Core operator nationallicence defect operator nationallicence Hilbert-Schmidt submodule nationallicence two variable Jordan block nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/3(2006-11-01), 431-449 0378-620X 56:3<431 2006 56 20 https://doi.org/10.1007/s00020-006-1422-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-006-1422-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yang Rongwei Department of Mathematics and Statistics, SUNY at Albany, 12222, Albany, NY, U.S.A aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/3(2006-11-01), 431-449 0378-620X 56:3<431 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer