an:03964786
Zbl 0598.47048
Mihailov, Dobrinca
On the procedures ''min'' and ''max'' for operator ideals on Banach couples
EN
Semin. Oper. Liniari Anal. Armonic??, Univ. Timi??oara 1, 9 p. (1984).
1984
j
47L10
generating new ideals; operator ideals on Banach couples; product; minimal kernel; ''min'' procedure; ''max'' procedure
One extends the procedures from \textit{A. Pietsch}, Operator ideals (1978; Zbl 0399.47039) of generating new ideals to the case of operator ideals on Banach couples.
The product of two operator ideals on Banach couples and the minimal kernel \({\mathcal A}^{\min}\) is defined. One shows the properties that result from the application of ''min'' procedure to the particular ideals.
The quotient \({\mathcal A}^{-1}\circ {\mathcal B}\) is also defined and the ''max'' procedure introduced. For closed operator ideals one shows that (\({\mathcal A}_ 1\wedge {\mathcal A}_ 2)^{\max}={\mathcal A}_ 1^{\max}\wedge {\mathcal A}_ 2^{\max}.\)
The following relations between two procedures are established:
\[
({\mathcal A}^{\min})^{\max}={\mathcal A}^{\max}\quad and\quad ({\mathcal A}^{\max})^{\min}={\mathcal A}^{\min}.
\]
Zbl 0399.47039