Spectral Inclusion Properties of Quaternionic Krein Space Numerical Range

被引：0

作者：

Mahfoudhi, Kamel ^{[1
]}

机构：

[1] Univ Sousse, Higher Inst Appl Sci & Technol, Comp Sci Dept, Sousse, Tunisia

来源：

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2023年 / 57卷 / SUPPL 1期

关键词：

quaternions; quaternionic Hilbert space; quaternionic Krein spaces; numerical range; quaternionic Krein space numerical range;

D O I：

10.1134/S0016266323050027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The article provides a concise overview of key concepts related to right quaternionic linear operators, quaternionic Hilbert spaces, and quaternionic Krein spaces. It then delves into the study of the quaternionic Krein space numerical range of a bounded right linear operator and the relationship between this numerical range and the S-spectrum of the operator. The article concludes by establishing spectral inclusion results based on the quaternionic Krein space numerical range and presenting the corresponding spectral inclusion theorems. In addition, we generalize some results to infinite dimensional quaternionic Krein spaces and give some examples.

引用

页码：17 / 25

页数：9

共 17 条

[1] The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum [J].

Alpay, Daniel ;

Colombo, Fabrizio ;

Kimsey, David P. .

JOURNAL OF MATHEMATICAL PHYSICS, 2016, 57 (02)

[2]

Alpay D, 2015, OPER THEORY ADV APPL, V244, P33

[3] Quaternionic numerical range of complex matrices [J].

Carvalho, Luis ;

Diogo, Cristina ;

Mendes, Sergio .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 620 :168-181

[4] A new perspective on the quaternionic numerical range of normal matrices [J].

Carvalho, Luis ;

Diogo, Cristina ;

Mendes, Sergio .

LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (20) :5068-5074

[5]

Colombo F, 2018, OPER THEORY ADV APPL, V270, P1, DOI 10.1007/978-3-030-03074-2

[6]

Colombo F, 2011, PROG MATH, V289, P1, DOI 10.1007/978-3-0348-0110-2

[7] On the formulations of the quaternionic functional calculus [J].

Colombo, Fabrizio ;

Sabadini, Irene .

JOURNAL OF GEOMETRY AND PHYSICS, 2010, 60 (10) :1490-1508

[8] Non Commutative Functional Calculus: Bounded Operators [J].

Colombo, Fabrizio ;

Gentili, Graziano ;

Sabadini, Irene ;

Struppa, Daniele C. .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2010, 4 (04) :821-843

[9]

Gustafson KE., 1997, Numerical range: the field of values of linear operators and matrices, DOI DOI 10.1007/978-1-4613-8498-4

[10] Quaternionic Davis-Wielandt Shell in a Right Quaternionic Hilbert Space [J].

Jeribi, Aref ;

Mahfoudhi, Kamel .

UKRAINIAN MATHEMATICAL JOURNAL, 2023, 75 (06) :897-907

← 1 2 →