Open Access

# On the numerical range with respect to a family of projections

### Abstract

In this note we introduce the concept of a numerical range of a bounded linear operator on a Hilbert space with respect to a family of projections. We give a precise definition and elaborate on its connection to the classical numerical range as well as to generalizations thereof such as the quadratic numerical range, block numerical range, and product numerical range. In general, the importance of this new notion lies within its unifying aspect.

Key words: Numerical range, bounded operator, spectrum.

### Article Information

 Title On the numerical range with respect to a family of projections Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 4, 297-304 MathSciNet MR3912067 Milestones Received 08/05/2018; Revised 06/08/2018 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

Department of Mathematics and Natural Sciences, 42119 Wuppertal, Germany

Joachim Kerner
Department of Mathematics and Computer Science, FernUniversitat in Hagen, 58084 Hagen, Germany

Nazife Erkurşun-Özcan
Department of Mathematics and Computer Science, Hacettepe University, 06800 Ankara, Turkey

### Citation Example

Waed Dada, Joachim Kerner, and Nazife Erkurşun-Özcan, On the numerical range with respect to a family of projections, Methods Funct. Anal. Topology 24 (2018), no. 4, 297-304.

### BibTex

@article {MFAT1111,
AUTHOR = {Waed Dada and Joachim Kerner and Nazife Erkurşun-Özcan},
TITLE = {On the numerical range with respect to a family of projections},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {4},
PAGES = {297-304},
ISSN = {1029-3531},
MRNUMBER = {MR3912067},
URL = {http://mfat.imath.kiev.ua/article/?id=1111},
}

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