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Operator ideal of type (p, q)

✍ Scribed by A. Račkauskas

Publisher
Springer
Year
1984
Tongue
English
Weight
672 KB
Volume
24
Category
Article
ISSN
0363-1672

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📜 SIMILAR VOLUMES

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✍ N.G. Van Kampen 📂 Article 📅 1958 🏛 Elsevier Science ⚖ 543 KB

It is shown that the operator p2 \_ q2 has a continuous spectrum extending from --00 to + oo. The expansion of an arbitrary function with respect to the eigenfunctions is given. The action of the operators q and p on the eigenfunctions can be written explicitly by means of symbolic formulae. Finally

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Operator Ideals Generalizing the Ideal of Strictly Singular Operators
✍ Irmtraud Stephani 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 675 KB

## Abstract It is well‐known that an operator __T__ ∈ L(__E, F__) is strictly singular if ∥__T__~__x__~∥≧λ∥__x__∥ on a subspace __Z__ ⊂ __E__ implies dim __Z__ < + ∞. The present paper deals with ideals of operators defined by a condition — ∥__T__~__x__~∥≧λ∥__x__∥ on an infinite‐dimensional subspac