TY - JOUR

T1 - Spaces of Operators Between Frechet Spaces

AU - Bonet, José

AU - Lindström, Mikael

N1 - Funding Information:
Proof, (a) is a consequence of Propositions 2 and 14 and the proofs of Theorem 3 (a) (1), (2) and (4). (b) follows directly from Proposition 14 and the proof of Theorem 3(a)(3). (c) The space lp+ has an unconditional basis and M(E,E) =)= L(E,E) by Example 6. The conclusion follows from Proposition 14. I The research of Jose Bonet was partially supported by the DGICYT Proyecto no. PB91-0538. The authors want to thank Pawel Domanski for his helpful remarks.

PY - 1994/1

Y1 - 1994/1

N2 - Motivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson-Nissenzweig theorem to Frechet spaces, we investigate pairs of Frechet spaces (E,F) such that every continuous linear map from E into F is Montel, i.e. it maps bounded subsets of E into relatively compact subsets of F. As a consequence of our results we characterize pairs of Kothe echelon spaces (E,F) such that the space of Montel operators from E into F is complemented in the space of all continuous linear maps from E into F.

AB - Motivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson-Nissenzweig theorem to Frechet spaces, we investigate pairs of Frechet spaces (E,F) such that every continuous linear map from E into F is Montel, i.e. it maps bounded subsets of E into relatively compact subsets of F. As a consequence of our results we characterize pairs of Kothe echelon spaces (E,F) such that the space of Montel operators from E into F is complemented in the space of all continuous linear maps from E into F.

UR - http://www.scopus.com/inward/record.url?scp=84974220807&partnerID=8YFLogxK

U2 - 10.1017/S0305004100071978

DO - 10.1017/S0305004100071978

M3 - Article

VL - 115

SP - 133

EP - 144

JO - Mathematical Proceedings

JF - Mathematical Proceedings

SN - 0305-0041

IS - 1

ER -