The Bishop-Phelps-Bollobás property represents a quantitative advancement of the classical Bishop-Phelps theorem. It asserts that if an operator on a Banach space nearly attains its norm at a ...

Banach spaces, being complete normed vector spaces, offer a versatile framework for analysing continuous linear operators and serve as a cornerstone of modern functional analysis. Their intrinsic ...

We investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the ...

Covered topics include Banach and Hilbert spaces, Hahn-Banach theorem, dual spaces, orthonormal bases, measure spaces, Lebesgue integration, convergence theorems, Lp-spaces and their duals, ...

The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach space with a Jordan structure. Far-reaching ...

Take as the Hahn-Banach theorem the property that f can be extended to a continuous linear functional on X without changing its norm. Innocent enough, but the ramifications of the theorem pervade ...

The Diocese of Arlington, Virginia, recently ordained 12 new Catholic priests in a joyful Mass at its cathedral.

Banach was hiking part of the Appalachian Trail with a small kit for the Eucharist in his pack. Tuesta was flying to Lima, Peru, his birthplace, to celebrate with family.

Dr. David Banach has dedicated nearly two decades to the field of infectious diseases and public health. With a background in medicine, research, and community service, he brings a holistic view of ...

We present new stability results for dynamical systems determined by a class of differential inclusions on Banach space. One of the results shows that under reasonable conditions, the same Lyapunov ...

Fermat’s Last Theorem is a mathematical conjecture about integer numbers, while the 3D Pythagoras’ theorem is a mathematical and geometrical proof about real numbers.