Factorization through inclusion mappings betweenl p-spaces

Jarchow, Hans

doi:10.1007/bf01351696

Cited by 8 publications

(1 citation statement)

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“…Another easy application concerns the ideals 3'p,9(l 5 p 5 q 5 00) of those operators which factor through the canonical injection J p , 9 : l p + l9 (see [3] for a thorough analysia of 3'p,9). The theorem shows …”

Section: P C Lmentioning

confidence: 99%

Limit Orders of ϵπ‐Continuous Operators

Defant

Mascioni

1990

Mathematische Nachrichten

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An operator T : X --f Y between BANACH spaces is said to be en-continuous if T 0 T : X @I X --+ Y an Y is continuous, where e and n denote the injective and projective topology, respectively. This concept was motivated by an old question of GROTHEN-DIECK asking for conditions to be imposed on a locally convex space E in order to ensure that E 0. E = E 0% E implies nuclearity of E (see [4] for details). Recently, new interest has been given to this question by PISIER's discovery of infinite dimensional BANACH spaces P such that P @ P = P 8% P (cf. [7]).In this note we compute the limit orders w, p , q) of the class of all en-continuougoperatorg, i.e., for 1 5 p, q I 00 the infimum over all A 1 0 such that each diagonal operator 0,: lp + lg with diagonal u E ia en-continuous. The main result ia:Theorem. Let p , q E [l, 003. Then Noreover, the limit order ie attained.1. Prelimiusries. We shall employ standard notations and notions from BANACH space theory end the theory of operator ideals, as preaented in [6].

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Section: P C Lmentioning

confidence: 99%