On Norm-Attainable Operators in Banach Spaces

Abstract

<jats:p>Norm-attainable operators have been studied over a period of time with nice results obtained particularly in Hilbert spaces. In this work, we consider the Banach space setting by characterizing nonpower operators on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>H</mml:mi></mml:math> and elementary operators. Lastly, we characterize a new notion of norm-attainability for power operators in general Banach spaces.</jats:p>

On Sharp Estimates of Coefficients for Polynomials in Norm-Attainable Classes

“…However, such studies have been done in different classes with a variety of estimates of coefficients obtained with varying degrees of sharpness [2]. Regarding norm-attainable classes, the characterization of several properties has been carried out (see [5] - [11]). These include the norm, numerical radius, spectral properties, and norm-attainability conditions [1].…”

On Characterization of Norm Attaining Operators in Frechet Spaces

“…Okelo [16] gave the characterizations of both the power and non-power operators considering the Banach space setting. They considered norm-attainability for inner derivation, generalized derivations and general elementary operators [17].…”