Let (en) be a complete orthonormal sequence in a Hilbert space H and let (2n) be a sequence of scalars. = (a) Show that there exists a unique operator T on H such that Ten λnen. (b) Show that T is bounded if and only if the sequence (2n) is bounded. (c) For a bounded sequence (2n), find the norm of T.

Let (en) be a complete orthonormal sequence in a Hilbert space H and let (2n) be a sequence of scalars. = (a) Show that there exists a unique operator T on H such that Ten λnen. (b) Show that T is bounded if and only if the sequence (2n) is bounded. (c) For a bounded sequence (2n), find the norm of T.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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