Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Representing non-weakly compact operators

100%

González M., Saksman E., Tylli H.-O.

Studia Mathematica

1995

tom 113

nr 3

265-282

For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E**/E) is defined by R(S)(x** + E) = S**x** + E(x** ∈ E**). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W(E) (here W(E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non-zero compact operators in Im(R) in the case of $L^1$ and C(0,1), but R(L(E)/W(E)) identifies isometrically with the class of lattice regular operators on $ℓ^2$ for $E = ℓ^2(J)$ (here J is James' space). Accordingly, there is an operator $T ∈ L(ℓ^2(J))$ such that R(T) is invertible but T fails to be invertible modulo $W(ℓ^2(J))$.

Ograniczanie wyników

1 Studia Mathematica

1 González M.

1 Saksman E.

1 Tylli H.-O.

1 1995

Wyniki wyszukiwania

Representing non-weakly compact operators