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We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.

A Banach space operator T ∈ has a left m-inverse (resp., an essential left m-inverse) for some integer m ≥ 1 if there exists an operator S ∈ (resp., an operator S ∈ and a compact operator K ∈ ) such that ${\sum }_{i=0}^m{(-1)}^i\left(\genfrac{}{}{0pt}{}{m}{i}\right)S^{m-i}{T}^{m-i}=0$ (resp., ${\sum }_{i=0}^m{(-1)}^i\left(\genfrac{}{}{0pt}{}{m}{i}\right)T^{m-i}{S}^{m-i}=K$). If $T_i$ is left $m_i$-invertible (resp., essentially left $m_i$-invertible), then the tensor product T₁ ⊗ T₂ is left (m₁ + m₂-1)-invertible (resp., essentially left (m₁ + m₂-1)-invertible). Furthermore, if T₁ is strictly left m-invertible (resp., strictly essentially left m-invertible), then...