The Spectral Property (ωπ): Equivalent Operators in Functionals, Families of Operators, and Tensor Products

The spectral property (ωπ) generalizes the a-Weyl theorem and characterizes the relationships between the spectrum and the upper semi-Fredholm spectrum. This paper proves that any nonzero scalar multiple of an operator verifying the property (ωπ) also satisfies it. Also, verify that Toeplitz and convolution operators satisfy this property, so infinitely many operators satisfy it. In this paper, we show that families of operators satisfying the property (ωπ) are upper semi-Fredholm static families. Finally, it is proved that the tensor product of two isoloid operators satisfying this property also satisfies it.