Lectures on Invariant Subspaces

Henry Helson

• Publisher: Academic Press
• Year: 2013
• Print ISBN: 9781483232072
• eBook ISBN: 9781483261522
• Topic: Mathematics
• Subtopic: Arithmetic
• Index: Mathematics

Lectures on Invariant Subspaces grew out of a series of lectures given gave at the University of Uppsala in the spring of 1962, and again in Berkeley the following semester. Since the subject is rather loosely defined the lecture style seemed appropriate also for this written version. The book is written for a graduate student who knows a little, but not necessarily very much, about analytic functions and about Hilbert space. The book contains 11 lectures and begins with a discussion of analytic functions. This is followed by lectures covering invariant subspaces, individual theorems, invariant subspaces in Lp, invariant subspaces in the line, and analytic vector functions. Subsequent lectures cover vectorial function theory, inner functions, range functions, and factoring of operator functions.

Table of contents

• Front Cover
• Lectures on Invariant Subspaces
• Copyright Page
• Table of Contents
• PREFACE
• LECTURE I. ANALYTIC FUNCTIONS
• LECTURE II. INVARIANT SUBSPACES
• LECTURE III. INDIVIDUAL THEOREMS
• LECTURE IV. INVARIANT SUBSPACES IN Lp
• LECTURE V. INVARIANT SUBSPACES ON THE LINE
• LECTURE VI. ANALYTIC VECTOR FUNCTIONS
• LECTURE VII. VECTORIAL FUNCTION THEORY
• LECTURE VIII. INNER FUNCTIONS
• LECTURE IX. RANGE FUNCTIONS
• LECTURE X. INVARIANT SUBSPACES (IN GENERAL)
• LECTURE XI. FACTORING OF OPERATOR FUNCTIONS
• References