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2002•高等学校计算数学学报：英文版Requires access

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

Chen, Guoliang, Wei, Musheng

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Abstract

In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.

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In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.

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Available abstract

In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.

Key concepts: Mathematics, Bounded inverse theorem, Banach space, Bounded function, Invertible matrix, Approximation property, Bounded operator, Finite-rank operator

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