Open Science Research Excellence

Fahui Zhai

Publications

3

Publications

3
10003230
Linear Maps That Preserve Left Spectrum of Diagonal Quaternionic Matrices
Abstract:
In this paper, we discuss some properties of left spectrum and give the representation of linear preserver map the left spectrum of diagonal quaternionic matrices.
Keywords:
Quaternionic matrix, left spectrum, linear preserver map.
2
10003650
Spherical Spectrum Properties of Quaternionic Operators
Abstract:
In this paper, the similarity invariant and the upper semi-continuity of spherical spectrum, and the spherical spectrum properties for infinite direct sums of quaternionic operators are characterized, respectively. As an application of some results established, a concrete example about the computation of the spherical spectrum of a compact quaternionic operator with form of infinite direct sums of quaternionic matrices is also given.
Keywords:
Spherical spectrum, Quaternionic operator, Upper semi-continuity, Direct sum of operators.
1
10006038
Necessary and Sufficient Condition for the Quaternion Vector Measure
Abstract:
In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.
Keywords:
Quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional.