Softcover ISBN:  9781470436247 
Product Code:  MEMO/260/1253 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470453237 
Product Code:  MEMO/260/1253.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470436247 
eBook: ISBN:  9781470453237 
Product Code:  MEMO/260/1253.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 
Softcover ISBN:  9781470436247 
Product Code:  MEMO/260/1253 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470453237 
Product Code:  MEMO/260/1253.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470436247 
eBook ISBN:  9781470453237 
Product Code:  MEMO/260/1253.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 260; 2019; 100 ppMSC: Primary 30; 47
In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprimeness of two singular inner functions and obtain several properties of the DouglasShapiroShields factorizations of matrix functions of bounded type. They propose a new notion of tensoredscalar singularity, and then answer questions on Hankel operators with matrixvalued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical HermiteFejér Interpolation Problem for matrix rational functions.
The authors then extend the \(H^\infty\)functional calculus to an \(\overline{H^\infty}+H^\infty\)functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrixvalued bounded type symbols and, in particular, the matrixvalued version of Halmos's Problem 5 and then establish a matrixvalued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of \(2\times 2\) partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrixvalued bounded type symbols and then derive rank formulae for the selfcommutators of hyponormal Toeplitz pairs.

Table of Contents

Chapters

1. Introduction

2. Preliminaries

3. Coprime inner functions

4. DouglasShapiroShields factorizations

5. Tensoredscalar singularity

6. An interpolation problem and a functional calculus

7. Abrahamse’s Theorem for matrixvalued symbols

8. A subnormal Toeplitz completion

9. Hyponormal Toeplitz pairs

10. Concluding remarks

List of Symbols


Additional Material

RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprimeness of two singular inner functions and obtain several properties of the DouglasShapiroShields factorizations of matrix functions of bounded type. They propose a new notion of tensoredscalar singularity, and then answer questions on Hankel operators with matrixvalued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical HermiteFejér Interpolation Problem for matrix rational functions.
The authors then extend the \(H^\infty\)functional calculus to an \(\overline{H^\infty}+H^\infty\)functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrixvalued bounded type symbols and, in particular, the matrixvalued version of Halmos's Problem 5 and then establish a matrixvalued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of \(2\times 2\) partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrixvalued bounded type symbols and then derive rank formulae for the selfcommutators of hyponormal Toeplitz pairs.

Chapters

1. Introduction

2. Preliminaries

3. Coprime inner functions

4. DouglasShapiroShields factorizations

5. Tensoredscalar singularity

6. An interpolation problem and a functional calculus

7. Abrahamse’s Theorem for matrixvalued symbols

8. A subnormal Toeplitz completion

9. Hyponormal Toeplitz pairs

10. Concluding remarks

List of Symbols