# Functional analysis: Quiz

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More interesting facts on Functional analysis

Question 1: The uniform boundedness principle (also known as ________) applies to sets of operators with uniform bounds.
Functional analysisBanach spaceTopological vector spaceUniform boundedness principle

Question 2: ________ can be completely classified: there is a unique Hilbert space up to isomorphism for every cardinality of the base.
Hilbert spaceVector spaceEigenvalue, eigenvector and eigenspaceMatrix (mathematics)

Question 3: These lead naturally to the definition of ________ and other operator algebras.
Von Neumann algebraHilbert spaceMatrix (mathematics)C*-algebra

Question 4: One of the open problems in functional analysis is to prove that every bounded linear operator on a Hilbert space has a proper ________.
Eigenvalue, eigenvector and eigenspaceInvariant subspaceVector spaceMatrix (mathematics)

Question 5: Functional analysis is the branch of ________, and specifically of analysis, concerned with the study of vector spaces and operators acting upon them.
MathematicsMathematical logicSet theoryGeometry

Question 6: Geometry of ________ contains many topics.
Vector spaceHilbert spaceComplete metric spaceBanach space

Question 7: In Banach spaces, a large part of the study involves the ________: the space of all continuous linear functionals.
Dual spaceLinear mapVector spaceHilbert space

Question 8: One is ________ approach connected with Jean Bourgain; another is a characterization of Banach spaces in which various forms of the law of large numbers hold.
MathematicsDiscrete mathematicsCombinatoricsCalculus

Question 9: These spaces are of fundamental importance in many areas, including the mathematical formulation of ________.
Wave–particle dualityQuantum mechanicsIntroduction to quantum mechanicsSchrödinger equation

Question 10: An important example is a ________, where the norm arises from an inner product.
Vector spaceMatrix (mathematics)Hilbert spaceEigenvalue, eigenvector and eigenspace