TY - JOUR

T1 - Approximation properties and some classes of operators

AU - Reinov, O. I.

N1 - Funding Information: Thus,thereexistsatleastoneoperatorU0∈A(Y;X)suchthata(U0)>1+εandtheimageJ(U0) belongs to the ∗-weak closure of the set J(Ba). However, the ∗-weak convergence in A∗∗(Y;X∗∗) implies the convergence in the weak operator topology. Therefore, there exists a net (Uν)ν ⊂ Y∗⊗˜aX such that a(Uν) ⩽ 1, (Uν) converges to U0 in the weak operator topology, but a(U0) > 1 + ε. In conclusion, we note that we may assume that ε is as large as we like. □ This work was partially supported by the Federal Program “INTEGRATSIYA” (grant No. 326.532) and the Swedish King Academy of Sciences.

PY - 2001

Y1 - 2001

N2 - The following questions and close problems are studied. (i) Is it true that T is p-nuclear provided that T** is p-nuclear? (ii) Is it true that T is dually p-nuclear provided that T* is p-nuclear? (iii) Is it true that if T* is compactly factorable in the space lp, then T is (strictly) factorable in the space lp′? Here, T* is the adjoint operator of a bounded operator T : X → Y in Banach spaces X and Y. Bibliography. 30 titles.

AB - The following questions and close problems are studied. (i) Is it true that T is p-nuclear provided that T** is p-nuclear? (ii) Is it true that T is dually p-nuclear provided that T* is p-nuclear? (iii) Is it true that if T* is compactly factorable in the space lp, then T is (strictly) factorable in the space lp′? Here, T* is the adjoint operator of a bounded operator T : X → Y in Banach spaces X and Y. Bibliography. 30 titles.

UR - http://www.scopus.com/inward/record.url?scp=52549100028&partnerID=8YFLogxK

U2 - 10.1023/A:1012392212102

DO - 10.1023/A:1012392212102

M3 - Article

VL - 107

SP - 3911

EP - 3951

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -