These notes present a theorem on infinite matrices with values in a topological group due to P. Antosik and J. Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinki, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikoym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in 1i and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.
FREE Two-Day Shipping for Students. Learn more |
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
(learn more)
First Sentence:
In the late 1960's Piotr Antosik was asked by Professor Jan Mikusinski to join in a project of completing the third part of the sequential theory of distributions developed by Professors Mikusinski and Sikorski in [MS1] and [MS2]. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Antosik-Mikusinski Theorem, Orlicz-Pettis Theorem, Banach-Steinhaus Theorem, Hahn-Schur Theorem, Uniform Boundedness Principle, Nikodym Boundedness Theorem, Nikodym Convergence Theorem, Closed Graph Theorem, Drewnowski's Lemma, Antosik Interchange Theorem, Antosik's Interchange Theorem, Baire Category Theorem, Hausdorff Abelian, Uniform Convergence Principle New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
In the late 1960's Piotr Antosik was asked by Professor Jan Mikusinski to join in a project of completing the third part of the sequential theory of distributions developed by Professors Mikusinski and Sikorski in [MS1] and [MS2]. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Antosik-Mikusinski Theorem, Orlicz-Pettis Theorem, Banach-Steinhaus Theorem, Hahn-Schur Theorem, Uniform Boundedness Principle, Nikodym Boundedness Theorem, Nikodym Convergence Theorem, Closed Graph Theorem, Drewnowski's Lemma, Antosik Interchange Theorem, Antosik's Interchange Theorem, Baire Category Theorem, Hausdorff Abelian, Uniform Convergence Principle New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 21
books:
See all 21 books this book cites
2
books
cite this book:
- Functional Analysis by K. C. Rao in Back Matter (1), and Back Matter (2)
- Functional Analysis (Springer Classics in Mathematics) by Kosaku Yosida in Back Matter
- Topological Vector Spaces, Distributions and Kernels (Dover Books on Mathematics) by Francois Treves in Back Matter
- A Course in Functional Analysis by John B. Conway in Back Matter
- Functional Analysis by Walter Rudin in Back Matter
See all 21 books this book cites
- The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh on page 232, and Back Matter
- The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh on page 232, and Back Matter
Tag this product(What's this?)Think of a tag as a keyword or label you consider is strongly related to this product.
Tags will help all customers organize and find favorite items. |
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
