Question: Who developed one of the foundations of functional analysis and also taught Hugo Steinhaus?

Context paragraphs:
Steinhaus longimeter: The Steinhaus longimeter, patented by the professor Hugo Steinhaus, is an instrument used to measure the lengths of curves on maps.  It is a transparent sheet of three grids, turned against each other by 30 degrees, each consisting of perpendicular lines spaced at equal distances 3.82 mm.  The measurement is done by counting crossings of the curve with grid lines.  The number of crossings is the approximate length of the curve in millimetres.

Studia Mathematica: Studia Mathematica is a Polish mathematics journal published since 1929.  It was founded by Stefan Banach and Hugo Steinhaus.  It accepts papers written in English, French, German, or Russian, primarily in functional analysis and related areas such as probability theory.

Steinhaus theorem: In the mathematical field of real analysis, the Steinhaus theorem states that the difference set of a set of positive measure contains an open neighbourhood of zero.  It was first proved by Hugo Steinhaus.

Hugo Steinhaus: Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator.  Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów (now Lviv, Ukraine), where he helped establish what later became known as the Lwów School of Mathematics.  He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem.  After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.

Axiom of determinacy: In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962.  It refers to certain two-person topological games of length ω.  AD states that every game of a certain type is determined; that is, one of the two players has a winning strategy.

Steinhaus–Johnson–Trotter algorithm: The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm, also called plain changes, is an algorithm named after Hugo Steinhaus, Selmer M. Johnson and Hale F. Trotter that generates all of the permutations of "n" elements.  Each permutation in the sequence that it generates differs from the previous permutation by swapping two adjacent elements of the sequence.  Equivalently, this algorithm finds a Hamiltonian path in the permutohedron.

Feliks Barański: Feliks Barański (1915-2006) was a Polish mathematician and an active member of the so-called Lwów School of Mathematics.  Born May 1915 in Lwów, Austria-Hungary (modern Lviv, Ukraine), he joined the circle of young, talented mathematicians formed around Stefan Banach and Hugo Steinhaus.  During the period of German occupation of his hometown he made his living as a lice feeder in the institute of Rudolf Weigl.  Expelled from Lwow after the war, he settled in Kraków, where he joined the local Kraków University of Technology.  He was also admitted into the Polish Mathematics Society.

Uniform boundedness principle: In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis.  Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field.  In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.

Functional analysis: Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.  The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces.  This point of view turned out to be particularly useful for the study of differential and integral equations.

David Hilbert: David Hilbert (] ; 23 January 1862 – 14 February 1943) was a German mathematician.  He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries.  Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry.  He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

Supporting paragraphs: Hugo Steinhaus David Hilbert
Answer: David Hilbert