S-Weyl’s theorem for bounded linear operators on Banach spaces

Key Points

• This research introduces S-Weyl’s theorem as a new variant of classical Weyl type theorems within Banach spaces.
• Investigated S-Weyl’s theorem along with a-Weyl’s theorem and property (w).
• Applied the theorem to several classes of operators, particularly Toeplitz operators.
• Focused on contexts involving the Hardy space H^{2} (T) over the unit circle.
• S-Weyl’s theorem encompasses the previously established a-Weyl’s theorem and property (w).
• The application to Toeplitz operators reveals specific conditions under which these operators satisfy the theorem.