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ON n-TUPLES OF TENSOR PRODUCTS OF p-HYPONORMAL OPERATORS

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Abstract

The operator A 2 L(Hi), the Banach algebra of bounded linear opera- tors on the complex in¯nite dimensional Hilbert space Hi, is said to be p-hyponormal if (A¤A)p ¸ (AA¤)p for p 2 (0; 1]. Let bH = H1\­¢ ¢ ¢­Hn denote the completion of H1­¢ ¢ ¢­Hn with respect to some crossnorm. Let Ii be the identity operator on Hi. Letting Ti := I1 ­¢ ¢ ¢­Ii¡1 ­Ai ­¢ ¢ ¢­In on bH, where each Ai is p-hyponormal, it is proved that the commuting n-tuple T = (T1; : : : ; Tn) satis¯es Bishop's condition (¯) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

참고문헌 (14)

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