Question: functional analysis course THEOREM (1) Let f be a bounded space linear functional defined on subspace M of a real normad linear subspace X.Then (1)

functional analysis course

THEOREM (1) Let f be a bounded space linear functional defined on subspace M of a real normad linear subspace X.Then (1) there exist a bounded linear functional F defined on X which extends f. And (2) ||F||=|lf||. THEOREM (2) Let X be a normad linear space and x* is not equal to 0 belong to X .Then there exist cartesian (bounded) linear functional f: X -:=- R such that (1) ||f||=1 and (2) f(x*]= ||x*||. Reference book introductory functional analysis with application by kreyszig

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related General Management Questions!

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

A creative engineer suggests structuring the TLB so that not all the bits of the presented address need match to result in a hit. Suggest how this might be achieved, and what might be the costs and...

Functional analysis Questions 81 17:36 - Expert Q&A W + 2. A subset M of a normed space X is said to be conver if x, y e M implies that { z EX : 2 = ax + ( 1 - c ) y, 0 s as1}cM, i.e. if the "line...

2. [25pts] (a) [9 pts) Show that the dual space (Co)' is isometrically isomorphic to l' (here co is a subspace of 1 consisting of sequences of scalars converging to zero). P.T.O 2 ZEZ (b) [8 pts)...

Exercise 2.3 Let ($2. E, u) be a positive finite measure space. Show that L, ($2, u()* can be identified with Lo($2, #). (This completes the proof of Theorem 2.13.) The following proves the theorem,...

"What would be the heart rate of a person if the cardiac output is 5 L, blood volume in the ventricles at the end of diastole is 100 ml. and at the end of ventricular systole is 50 ml, ? 50 beats per...

Rebecca Taylor, an international equity portfolio manager, recognizes that an optimal country allocation strategy combined with an optimal currency strategy should produce optimal portfolio...

Sastri Novelties Ltd , a South African technology company, has provided the following financial information for its fiscal year ending 3 1 December 2 0 2 3 . The company has both ordinary and...

Quick please thanks Manufacturing incorpotated Mi) purchased land on 1 January 202, which it started to operate as a gravel pit. The gravel pit will be operating for the next 22 years At the end of...