Commun. Korean Math. Soc. 2023; 38(4): 1127-1139
Online first article October 16, 2023 Printed October 31, 2023
Copyright © The Korean Mathematical Society.
Asuman Guven Aksoy, Daniel Akech Thiong
Claremont McKenna College; Claremont Graduate University
We investigate an extension of Schauder's theorem by studying the relationship between various $s$-numbers of an operator $T$ and its adjoint $T^*$. We have three main results. First, we present a new proof that the approximation number of $T$ and $T^*$ are equal for compact operators. Second, for non-compact, bounded linear operators from $X$ to $Y$, we obtain a relationship between certain $s$-numbers of $T$ and $T^*$ under natural conditions on $X$ and $Y$. Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of $T$ with that of its adjoint $T^*$.
Keywords: $s$-numbers, approximation schemes, Schauder's theorem
MSC numbers: Primary 47B06, 47B10; Secondary 47B07
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd