Compact and Nuclear Maps on Power Series Spaces

✍ Scribed by M. S. Ramanujan; T. Terzioglu

• Publisher: John Wiley and Sons
• Year: 1979
• Tongue: English
• Weight: 300 KB
• Volume: 93
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19790930113

✦ Synopsis

RAMANUJAN of Ann Arbor (USA) and T. TERZIOCLU of Ankara (Turkey) (Eingegangen am 2. 1. 1978)

I n this note we give two (unrelated) results; the first is a necessary and sufficient condition for a matrix map on a KOTHE space A(P) into another, A(&), to be A(&)-nuclear; the second is that the eigenvalues of a compact endomorphism on a A,(E)-nuclear space, and in particular on A-(E), can be arranged into an element of A-(a). This is based on an extended WEYL'S inequality for operators on a HILBERT space; a version of this for BANACH spaces (due essentially to H. KONIG) is also included.

The definitions explicitly stated are kept a t a minimum; the reader is referred to KOTHE [5] and PIETSCH [7] for various terminologies which are more common. A-nuclear maps, G--spaces (also called spaces A(P), P a power set) are defined in [l, 111; A,(cr)-nuclearity is defined in [9]. P K spaces are found in [12]. Diametral dimension is used as defined in [Ill.