Let X = d v p and Y = d w q be Lorentz sequence spaces. We investigate when the space K X Y of compact linear operators acting from X to Y forms or does not form an M-ideal (in the space of bounded linear operators). We show that K X Y fails to be a non-trivial M-ideal whenever p = 1 or p > q. In th
On the Lorentz-Marcinkiewicz Operator Ideal
β Scribed by Fernando Cobos Madrid
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 966 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
This article deals with the LORENTZ-MARCINKIEWICZ operator ideal 2Eb, generated by an additive a-function and the LORENTZ-MARCINEIEWICZ sequence space Aq(p). We give eigenvalue distributions for operators belonging to B$b(E, E ) and we show the interpolation properties of Bt;-ideals. Furthermore, we study certain SCHAIJDER bases in 2E:(H, K ) , H and K HILBEBT spaces.
π SIMILAR VOLUMES
We find a new expression for the norm of a function in the weighted Lorentz space, with respect to the distribution function, and obtain as a simple consequence a generalization of the classical embeddings \(L^{r, 1} \subset \cdots \subset L^{p} \subset \cdots \subset L^{p . r}\) and a new definitio
## Abstract It is wellβknown that an operator __T__ β L(__E, F__) is strictly singular if β₯__T__~__x__~β₯β§Ξ»β₯__x__β₯ on a subspace __Z__ β __E__ implies dim __Z__ < + β. The present paper deals with ideals of operators defined by a condition β β₯__T__~__x__~β₯β§Ξ»β₯__x__β₯ on an infiniteβdimensional subspac
## On the Spectrum of Products of Operator Ideals By HERMANN KONIG \*) of Bonn (Eingegangen am 10. 3.1978) The eigenvalues of absolutely p-summing ( 2 ~p -=-) and type lp operators (0 <p-=-) in BANACH spaces are p-th power summable. I n this note, we deal with operators which can be factored as p