On normal extensions of unbounded operators. IV: A matrix construction. (English) Zbl 1106.47021

Langer, Matthias (ed.) et al., Operator theory and indefinite inner product spaces. Presented on the occasion of the retirement of Heinz Langer in the colloquium on operator theory, Vienna, March 2004. Basel: Birkhäuser (ISBN 3-7643-7515-9/hbk). Operator Theory: Advances and Applications 163, 337-350 (2006).
For parts I to III, see [J. Oper. Theory 14, 31–55 (1985; Zbl 0613.47022); Acta Sci. Math. 53, No. 1/2, 153–177 (1989; Zbl 0698.47003); Publ. Res. Inst. Math. Sci. 25, No. 1, 105–139 (1989; Zbl 0721.47009)].
A condition for an unbounded operator to have a normal extension, which is a matrix operator, is given. The circumstances under which this condition may become necessary are discussed as well and, finally, a question is posed. Along the way, some substantial facts concerning infinite operator matrices with unbounded entries are gathered.
For the entire collection see [Zbl 1086.47007].


47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B20 Subnormal operators, hyponormal operators, etc.
47A20 Dilations, extensions, compressions of linear operators