#### 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

*R*^{n}(*A*) =
{*V*^{*}*AW* :
*V,W* : **C**^{n}
→
*H*, *V*^{*}*V* =
*W*^{*}*W* = *I*_{n},
*V*^{*}*W* = 0}.

It is shown that the closed matricial convex hull of
*R*^{n}(*A*) is a closed ball
of radius
min {|*A* -
λ*I*| :
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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