대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권4호
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  • Pages.1127-1139
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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EQUALITY IN DEGREES OF COMPACTNESS: SCHAUDER'S THEOREM AND s-NUMBERS

  • 투고 : 2023.01.07
  • 심사 : 2023.05.19
  • 발행 : 2023.10.31
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초록

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*.

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참고문헌

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