Lecture Notes in Functional Analysis

by William L. Paschke

edition 0.9

Contents

Frontmatter

I. Hilbert Space

II. Bounded Operators

III. Compact Operators

IV. The Spectral Theorem

Index and References

## Index

 Banach space
 Calkin algebra Cauchy sequence
 Hilbert space Hilbert space tensor product  $$$H\mathbin{\hat{\otimes}} K$$$ Hilbert-Schmidt operator
 Volterra Operator
 adjoint  $$$T^{*}$$$ algebraic tensor product  $$${V}_{1}\otimes \dotsb\otimes {V}_{n}$$$
 bounded linear operator
 closable linear operator closed linear operator closure of linear operator  $$$\overline{L}$$$ compact operator complete metric space complex group algebra  $$$\mathbb{C}G$$$ conjugate linear cyclic subspace cyclic vector complex unit circle  $$$\mathbb{T}$$$
 direct sum  $$$U\oplus W$$$ distance to subset  $$$\operatorname{d}$$$ dual space  $$${X}^{*}$$$
 essential supremum  $$$\mathopen{}\left\lVert{}φ\right\rVert_\infty\mathclose{}$$$ extension external direct sum  $$${H}_{1}\oplus \dotsb\oplus {H}_{n}$$$
 finite rank
 graph  $$$\mathop{\mathcal{G}}$$$
 inner product  $$$\mathopen{}\left\langle{}\cdot, \cdot\right\rangle\mathclose{}$$$ inner product space integral operator isometry isomorphism  $$$H\simeq K$$$
 metric metric space multilinear multiplication operator
 norm  $$$\mathopen{}\left\lVert{}\cdot\right\rVert\mathclose{}$$$ normal operator normed algebra normed linear space null vector
 open orthogonal  $$$x\perp y$$$ orthogonal complement  $$${S}^{\perp}$$$ orthogonal complement in subspace  $$$T\ominus {T}_{1}$$$ orthogonal projection orthonormal orthonormal basis orthogonal projection operator
 p-norm  $$$\mathopen{}\left\lVert{}f\right\rVert_p\mathclose{}$$$ partial isometry positive operator positive definite matrix positive definite function positive sesquilinear form  $$$\mathopen{}\left\langle{}\cdot, \cdot\right\rangle\mathclose{}$$$ projection
 quotient space  $$$V/S$$$
 resolution of the identity
 self-adjoint operator simple tensors spectral radius  $$$\mathop{\rho}$$$ spectral resolution spectrum  $$$\mathop{\sigma}$$$ supremum norm  $$$\mathopen{}\left\lVert{}f\right\rVert_\infty\mathclose{}$$$
 trace-class operator
 ultraweak topology unitary operator
 weak*-topology  $$$\mathop{\mathrm{w}^*}$$$

## References

[1]Bachman, George; Narici, Lawrence; Functional analysis. Academic Press, New York. 1966.

[2]Friedman, Avner; Foundations of modern analysis. Holt, Rinehart and Winston, Inc., New York. 1970.

[3]Gohberg, Israel; Goldberg, Seymour; Krupnik, Nahum; Traces and determinants of linear operators. Birkhäuser Verlag, Basel. 2000.

[4]Istrăţescu, Vasile Ion; Inner product structures. D. Reidel Publishing Co., Dordrecht. 1987.

[5]Kadison, Richard V.; Ringrose, John R.; Fundamentals of the theory of operator algebras. Vol. I. American Mathematical Society, Providence, RI. 1997.

[6]Kadison, Richard V.; Ringrose, John R.; Fundamentals of the theory of operator algebras. Vol. II. American Mathematical Society, Providence, RI. 1997.

[7]Köthe, Gottfried; Topological vector spaces. I. Springer-Verlag New York, Inc., New York. 1969.

[8]Murphy, Gerard J.; C*-algebras and operator theory. Academic Press, Inc., Boston, MA. 1990.

[9]Rickart, Charles E.; General theory of Banach algebras. D. Van Nostrand Co., Inc., Princeton, N.J.. .

[10]Rudin, Walter; Principles of mathematical analysis. McGraw-Hill Book Co., New York. 1976.

[11]Yosida, Kôsaku; Functional analysis. Springer-Verlag, New York. 1974.

[12]Young, Nicholas; An introduction to Hilbert space. Cambridge University Press, Cambridge. 1988.