Research

My research lies in Functional Analysis and Operator Theory, with a focus on Banach space geometry, numerical index theory, Bishop–Phelps–Bollobás type properties, tensor product spaces, and spectral and algebraic properties of operators.

Numerical Index Theory

I study numerical index and numerical radius problems in Banach spaces, including questions related to convergence, stability, and behavior under constructions such as operator openings and ultraproducts.

• On the Convergence of Numerical Index via Operator Openings and Ultraproducts, 2026.
• The numerical index of ℓ_p², 2022.

Bishop–Phelps–Bollobás Type Properties

I am interested in quantitative norm-attainment properties for operators, particularly Bishop–Phelps–Bollobás type properties for spaces of continuous functions and related Banach spaces.

• The Bishop–Phelps–Bollobás Property for Extremally Disconnected Ranges: Separable and Low-Density Domains, 2026.

Tensor Product Spaces and Quotient Problems

I study projective tensor products, quotient maps, lifting properties, and the interaction between tensor products, subspaces, and quotient spaces.

• Quotients of tensor product spaces, 2019.
• The Existence of Linear Selection and the Quotient Lifting Property, 2021.

Operator Theory and n-Potent Operators

I am also interested in algebraic and spectral properties of operators satisfying polynomial identities, including n-potent operators and projections in algebras generated by such operators.

• Projections in the Algebra Generated by an n-Potent Operator, 2025.