Vol. 66, No. 1, 1976

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On generalized numerical ranges

S. M. Patel

Vol. 66 (1976), No. 1, 235–241

The Luecke’s class of operators T on a Hilbert space H for which (T vI)1= 1∕d(v,W(T)), vCLW (T), where CLW (T) is the closure of the numerical range W(T) of T, has been generalized by using the concept of generalized numerical ranges due to C. S. Lin. Also it has been shown that the notions of generalized Minkowski distance functionals and generalized numerical ranges arise in a natural way for elements of the Calkin algebra.

Mathematical Subject Classification 2000
Primary: 47A10
Received: 6 February 1975
Revised: 2 April 1976
Published: 1 September 1976
S. M. Patel