Glasnik Matematicki, Vol. 39, No.1 (2004), 139-144.

A GENERALIZATION OF THE 0-NUMERICAL RANGE

Rajna Rajić

Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
e-mail: rajna.rajic@zg.hinet.hr


Abstract.   Let H be a complex Hilbert space. Given a bounded linear operator A on H, we describe the set

Rn(A) = {V*AW : V,W : Cn H, V*V = W*W = In, V*W = 0}.

It is shown that the closed matricial convex hull of Rn(A) is a closed ball of radius

min {|A - λI| : λ ∈ C}

centered at the origin.

2000 Mathematics Subject Classification.   47A12.

Key words and phrases.   q-numerical range of an operator.


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