IJPAM: Volume 64, No. 1 (2010)
EQUAL TO THE SUM OF THEIR NORMS
Department of Mathematics
2600 College St., Sherbrooke, QC, J1M 1Z7, CANADA
Abstract.In this paper we first characterize the norm of the sum of vectors in a normed linear space being equal to the sum of their norms. These results make it possible to characterize the norm of the sum of bounded linear operators in a normed linear space being equal to the sum of their norms. Many interesting results about approximate eigenvalues follows. In applications, these results are characterized in terms of numerical ranges for operators in Hilbert spaces.
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Received: August 16, 2010
AMS Subject Classification: 47A10, 47A30, 47A50
Key Words and Phrases: uniformly convex space, strictly convex space, Daugavet equation, isometric isomorphism, numerical range of operator and its closure, complete vector for operator, norm attaining vector for operator, eigenvalue and approximate eigenvalue of operator
Source: International Journal of Pure and Applied Mathematics