Gene

Nuclear operator

Banach space

Product (mathematics)

Engineering

Pure mathematics

Discrete mathematics

Statistics

Joint (building)

Hilbert space

Biochemistry

Computer science

Bounded function

Spectral theorem

Tensor (intrinsic definition)

Mathematics

Tensor product

Transcription factor

Mathematical analysis

Artificial intelligence

Geometry

Structural engineering

Repressor

Architectural engineering

Chemistry

Normality

Operator (biology)

Class (philosophy)

Operator theory

Tuple

Finite-rank operator

Linear and Multilinear Algebra

In this paper, we introduce the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space H when an additional semi-inner product induced by a positive operator A is considered. We investigate this new class of operators which is called A-normal d-tuple of operators. Mainly, we study the tensor product and the tensor sum of two A-normal d-tuples of operators. Also, we define the A-joint spectral radius associated with a d-tuple T=(T1,…,Td) denoted rA(T) and we show that under some conditions we have rA(T)=|||T|||A, where |||T|||A denotes the A-joint operator seminorm of T.

Joint normality of operators in semi-Hilbertian spaces