Algebra and Analysis for Engineers and Scientists pp 343-405 | Cite as

# Normed Spaces and Inner Product Spaces

## Abstract

In Chapters 2–4 we concerned ourselves primarily with algebraic aspects of certain mathematical systems, while in Chapter 5 we addressed ourselves to topological properties of some mathematical systems. The stage is now set to combine topological and algebraic structures. In doing so, we arrive at linear topological spaces, namely normed linear spaces and inner product spaces, in general, and Banach spaces and Hilbert spaces, in particular. The properties of such spaces are the topic of the present chapter. In the next chapter we will study linear transformations defined on Banach and Hilbert spaces. The material of the present chapter and the next chapter constitutes part of a branch of mathematics called **functional analysis**.

## Keywords

Hilbert Space Banach Space Linear Space Normed Space Linear Subspace## Preview

Unable to display preview. Download preview PDF.

## References

- [6.1]F. W. Byron and R. W. Fuller,
*Mathematics of Classical and Quantum Physics*, Vols. I, II. Reading, Mass.: Addison-Wesley Publishing Co., Inc., 1969 and 1970.MATHGoogle Scholar - [6.2]N. Dunford and J. Schwartz,
*Linear Operators*. Parts I and II. New York: Interscience Publishers, 1958 and 1964.MATHGoogle Scholar - [6.3]P. R. Halmos,
*Introduction to Hilbert Space*. New York: Chelsea Publishing Company, 1957.MATHGoogle Scholar - [6.4]E. Hille and R. S. Phillips,
*Functional Analysis and Semi-Groups*. Providence, R.I.: American Mathematical Society, 1957.Google Scholar - [6.5]R. E. Kalman, P. L. Falb, and M. A. Arbib,
*Topics in Mathematical System Theory*. New York: McGraw-Hill Book Company, 1969.MATHGoogle Scholar - [6.6]L. V. Kantorovich and G. P. Akilov,
*Functional Analysis in Normed Spaces*. New York: The Macmillan Company, 1964.MATHGoogle Scholar - [6.7]A. N. Kolmogorov and S. V. Fomin,
*Elements of the Theory of Functions and Functional Analysis*. Vols. I, II. Albany, N.Y.: Graylock Press, 1957 and 1961.Google Scholar - [6.8]L. A. Liusternik and V. J. Sobolev,
*Elements of Functional Analysis*. New York: Frederick Ungar Publishing Company, 1961.Google Scholar - [6.9]D. G. Luenberger,
*Optimization by Vector Space Methods*. New York: John Wiley & Sons, Inc., 1969.MATHGoogle Scholar - [6.10]A. W. Naylor and G. R. Sell,
*Linear Operator Theory*. New York: Holt, Rinehart and Winston, 1971.Google Scholar - [6.11]W. A. Porter,
*Modern Foundations of Systems Engineering*. New York: The Macmillan Company, 1966.Google Scholar - [6.12]A. E. Taylor,
*Introduction to Functional Analysis*. New York: John Wiley & Sons, Inc., 1958.MATHGoogle Scholar - [6.13]