The <i>K</i>_{<i>p</i>,<i>q</i>}-Compactness and <i>K</i>_{<i>p</i>,<i>q</i>}-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces

Abstract

Let Kp,q (1≤p,q≤∞ with 1/p+1/q≥1) be the ideal of (p,q)-compact operators. This paper investigates the compactness and null sequences via Kp,q, and an approximation property of the ideal of Kp,q-compact operators.

Keywords

• compact set
• null sequence
• (<i>p</i>,<i>q</i>)-compact operator
• Banach operator ideal
• approximation property