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Softcover ISBN:  9781470442385 
Product Code:  MEMO/267/1297 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
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Product Code:  MEMO/267/1297.E 
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AMS Member Price:  $68.00 
Softcover ISBN:  9781470442385 
eBook ISBN:  9781470463939 
Product Code:  MEMO/267/1297.B 
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MAA Member Price:  $153.00 $114.75 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 267; 2020; 101 ppMSC: Primary 47
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory.
The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right but also a leftmultiplication on the considered Banach space \(V\). This has technical reasons, as the space of bounded operators on \(V\) is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.

Table of Contents

Chapters

1. Introduction

2. Preliminaries

3. Slice Hyperholomorphic Functions

4. The SFunctional Calculus

5. The Spectral Theorem for Normal Operators

6. Intrinsic SFunctional Calculus on OneSided Banach Spaces

7. Spectral Integration in the Quaternionic Setting

8. On the Different Approaches to Spectral Integration

9. Bounded Quaternionic Spectral Operators

10. Canonical Reduction and Intrinsic SFunctional Calculus for Quaternionic Spectral Operators

11. Concluding Remarks


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Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory.
The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right but also a leftmultiplication on the considered Banach space \(V\). This has technical reasons, as the space of bounded operators on \(V\) is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.

Chapters

1. Introduction

2. Preliminaries

3. Slice Hyperholomorphic Functions

4. The SFunctional Calculus

5. The Spectral Theorem for Normal Operators

6. Intrinsic SFunctional Calculus on OneSided Banach Spaces

7. Spectral Integration in the Quaternionic Setting

8. On the Different Approaches to Spectral Integration

9. Bounded Quaternionic Spectral Operators

10. Canonical Reduction and Intrinsic SFunctional Calculus for Quaternionic Spectral Operators

11. Concluding Remarks