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Instructions to follow: * Give original work "Support your work with examples and graphs where required * Follow The references: Kreyszig, Rudin and Robert. G. Bartle. Reference Books: C.D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, 3rd Edition, Harcourt Asia, (2000) J. Bak and D.J. Newman, Complex Analysis, 2nd Edition, Springer Indian Reprint, (2009) Bartle and Sherbert, Introductory Real Analysis, 3rd edition, Wiley International, (2001) Hahn-Banach Theorem Extensions Question: State and prove the Hahn-Banach theorem in both its algebraic and analytic forms. Then, provide a proof of the theorem when applied to complex vector spaces. Conclude by discussing an application of the Hahn-Banach theorem in dual space theory. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Singapore Edition, Banach-Alaoglu Theorem (2001). S. Kumaresan, Topology of Metric Spaces, Narosa, (2005). S. Kumaresan, Real Analysis An Outline, Unpublished Course Notes (available at http://mtta.org.in/downloads) B.V. Limaye, Functional Analysis, 2nd Edition, New Age International Ltd., (1996). W. Rudin, Rea! and Complex Analysis, TMH Edition, 1973. Question: Prove the Banach-Alaoglu theorem, which states that the closed unit ball in the dual space of a normed vector space is compact in the weak-* topology. Use Tychonoff's theorem as part of your proof, and explore its applications in reflexive spaces. Throughout these notes we let IK We use the symbol for example.

Instructions to follow: * Give original work "Support your work with examples and graphs where required * Follow The references: Kreyszig, Rudin and Robert. G. Bartle. Reference Books: C.D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, 3rd Edition, Harcourt Asia, (2000) J. Bak and D.J. Newman, Complex Analysis, 2nd Edition, Springer Indian Reprint, (2009) Bartle and Sherbert, Introductory Real Analysis, 3rd edition, Wiley International, (2001) Hahn-Banach Theorem Extensions Question: State and prove the Hahn-Banach theorem in both its algebraic and analytic forms. Then, provide a proof of the theorem when applied to complex vector spaces. Conclude by discussing an application of the Hahn-Banach theorem in dual space theory. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Singapore Edition, Banach-Alaoglu Theorem (2001). S. Kumaresan, Topology of Metric Spaces, Narosa, (2005). S. Kumaresan, Real Analysis An Outline, Unpublished Course Notes (available at http://mtta.org.in/downloads) B.V. Limaye, Functional Analysis, 2nd Edition, New Age International Ltd., (1996). W. Rudin, Rea! and Complex Analysis, TMH Edition, 1973. Question: Prove the Banach-Alaoglu theorem, which states that the closed unit ball in the dual space of a normed vector space is compact in the weak-* topology. Use Tychonoff's theorem as part of your proof, and explore its applications in reflexive spaces. Throughout these notes we let IK We use the symbol for example.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 5E
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Instructions to follow: * Give original work "Support your work with examples and graphs where required * Follow The references: Kreyszig, Rudin and Robert. G. Bartle. Reference Books: C.D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, 3rd Edition, Harcourt Asia, (2000) J. Bak and D.J. Newman, Complex Analysis, 2nd Edition, Springer Indian Reprint, (2009) Bartle and Sherbert, Introductory Real Analysis, 3rd edition, Wiley International, (2001) Hahn-Banach Theorem Extensions Question: State and prove the Hahn-Banach theorem in both its algebraic and analytic forms. Then, provide a proof of the theorem when applied to complex vector spaces. Conclude by discussing an application of the Hahn-Banach theorem in dual space theory. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Singapore Edition, Banach-Alaoglu Theorem (2001). S. Kumaresan, Topology of Metric Spaces, Narosa, (2005). S. Kumaresan, Real Analysis An Outline, Unpublished Course Notes (available at http://mtta.org.in/downloads) B.V. Limaye, Functional Analysis, 2nd Edition, New Age International Ltd., (1996). W. Rudin, Rea! and Complex Analysis, TMH Edition, 1973. Question: Prove the Banach-Alaoglu theorem, which states that the closed unit ball in the dual space of a normed vector space is compact in the weak-* topology. Use Tychonoff's theorem as part of your proof, and explore its applications in reflexive spaces. Throughout these notes we let IK We use the symbol for example.
Transcribed Image Text:Instructions to follow: * Give original work "Support your work with examples and graphs where required * Follow The references: Kreyszig, Rudin and Robert. G. Bartle. Reference Books: C.D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, 3rd Edition, Harcourt Asia, (2000) J. Bak and D.J. Newman, Complex Analysis, 2nd Edition, Springer Indian Reprint, (2009) Bartle and Sherbert, Introductory Real Analysis, 3rd edition, Wiley International, (2001) Hahn-Banach Theorem Extensions Question: State and prove the Hahn-Banach theorem in both its algebraic and analytic forms. Then, provide a proof of the theorem when applied to complex vector spaces. Conclude by discussing an application of the Hahn-Banach theorem in dual space theory. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Singapore Edition, Banach-Alaoglu Theorem (2001). S. Kumaresan, Topology of Metric Spaces, Narosa, (2005). S. Kumaresan, Real Analysis An Outline, Unpublished Course Notes (available at http://mtta.org.in/downloads) B.V. Limaye, Functional Analysis, 2nd Edition, New Age International Ltd., (1996). W. Rudin, Rea! and Complex Analysis, TMH Edition, 1973. Question: Prove the Banach-Alaoglu theorem, which states that the closed unit ball in the dual space of a normed vector space is compact in the weak-* topology. Use Tychonoff's theorem as part of your proof, and explore its applications in reflexive spaces. Throughout these notes we let IK We use the symbol for example.
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