Contributions to Functional Analysis by Harro Heuser, R. E. Fullerton, C. C. Braunschweiger, Ebbe

By Harro Heuser, R. E. Fullerton, C. C. Braunschweiger, Ebbe Thue Poulsen, Jean Leray, Gregers Krabbe, Anastasios Mallios, Tosio Kato, Felix E. Browder, Takako Kōmura, Yukio Kōmura, Helmut H. Schaefer, Kosaku Yosida, Nelson Dunford, Joseph Nieto, W. A. J. Lu

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Eingegangen am 9. Miirz 1965) DIAz, J. B. and F. T. METCALF Math. Annalen 162, 120-139 {1965) Complementary Inequalities ID: Inequalities Complementary to Schwarz's Inequality in Hilbert Space* Dedicated to Professor GoTTFRIED KoTHE on the occasion of his sixtieth birthday, December 25, 1965 By J. B. Duz and F. T. METCALF** in College Park, Maryland Introduction The Schwarz inequality [18, p. 198] in a Hilbert space (with real or complex scalars) implies that I(Ax, Bx)i2 ~ (Ax, Ax) (Bx, Bx), where xis an arbitrary vector of the Hilbert space, A and Bare operators on the Hilbert space to itself.

Dann ist

Es werde nun gezeigt: Die Zusammenziehung wird durch die heiden Verformungen T,A, die jedes A in T 1 A iiberfiihrt, und (1 - s) T 1 A + slf' A 0 , bei der T 1 A in If' A 0 iibergeht, geleistet. Es bleibt dabei offenbar nur noch zu beweisen, daB (1- s) T 1 A + slf' A 0 immer in

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