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2015•Asian Journal of Fuzzy and Applied MathematicsRequires access

On Bounded Linear Operations in b-Hilbert Spaces and their Numerical Ranges

Mahnaz Khanehgir, Firoozeh Hasanvand

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Abstract

In this paper, we introduce the notions of b-bounded linear operator, b-numericalrange and b-numerical radius in a b-Hilbert space and describe some of their properties. Thenwe will show that this new numerical range (radius) can be considered as a usual numericalrange (radius) in a Hilbert space, so it shares many useful properties with numerical range(radius).

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What this paper is about

In this paper, we introduce the notions of b-bounded linear operator, b-numericalrange and b-numerical radius in a b-Hilbert space and describe some of their properties. Thenwe will show that this new numerical range (radius) can be considered as a usual numericalrange (radius) in a Hilbert space, so it shares many useful properties with numerical range(radius).

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Available abstract

In this paper, we introduce the notions of b-bounded linear operator, b-numericalrange and b-numerical radius in a b-Hilbert space and describe some of their properties. Thenwe will show that this new numerical range (radius) can be considered as a usual numericalrange (radius) in a Hilbert space, so it shares many useful properties with numerical range(radius).

Key concepts: Hilbert space, Bounded function, Bounded operator, Mathematics, Numerical range, RADIUS, Linear operators, Range (aeronautics)

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