NDLI: On Ptak's Generalization of Hankel Operators

Content Provider	Springer Nature Link
Author	Mancera, Carmen H. Paul, Pedro J.
Copyright Year	2001
Abstract	In 1997 Ptak defined generalized Hankel operators as follows: Given two contractions $$T_1 \in \mathcal{B}(\mathcal{H}_1 )$$ and $$T_2 \in \mathcal{B}(\mathcal{H}_2 )$$ , an operator $$X:\mathcal{H}_1 \to \mathcal{H}_2 $$ is said to be a generalized Hankel operator if $$T_2 X = XT_1^* $$ and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of T 1 and T 2. This approach, call it (P), contrasts with a previous one developed by Ptak and Vrbova in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat hidden connection between the theories (P) and (PV) and we clarify that connection by proving that (P) is more general than (PV), even strictly more general for some T 1 and T 2, and by studying when they coincide. Then we characterize the existence of Hankel operators, Hankel symbols and analytic Hankel symbols, solving in this way some open problems proposed by Ptak.
Starting Page	323
Ending Page	342
Page Count	20
File Format	PDF
ISSN	00114642
Journal	Czechoslovak Mathematical Journal
Volume Number	51
Issue Number	2
e-ISSN	15729141
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2001-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Analysis Ordinary Differential Equations Mathematical Modeling and Industrial Mathematics Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Mathematics

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