# Lp space: Quiz

Question 1: The fact that Lp is complete is often referred to as ________.
Hilbert spaceBanach spaceRiesz–Fischer theoremLp space

Question 2: For 1 ≤ p ≤ ∞, Lp(S, μ) is a ________.
Vector spaceBanach spaceHilbert spaceComplete metric space

Question 3: When p = 2; like the ℓ2 space, the space L2 is the only ________ of this class.
Hilbert spaceVector spaceMatrix (mathematics)Eigenvalue, eigenvector and eigenspace

Question 4: They form an important class of examples of ________ in functional analysis, and of topological vector spaces.
Complete metric spaceMetric spaceBanach spaceHilbert space

Question 5:
Which of the following titles did Lp space have?
 Proof that Lp spaces are complete 2008 Khurcha incident Howard Chaykin Rock-n-Roll Pizzeria

Question 6: If we use complex-valued functions, the space L is a commutative ________ with pointwise multiplication and conjugation.
Matrix (mathematics)Hilbert spaceVon Neumann algebraC*-algebra

Question 7: The additional inner product structure allows for a richer theory, with applications to, for instance, ________ and quantum mechanics.
Fourier seriesFourier analysisHilbert spaceFourier transform

Question 8: In ________, the Lp spaces are function spaces defined using natural generalizations of p-norms for finite-dimensional vector spaces.
Set theoryMathematicsMathematical logicGeometry

Question 9: If p is a ________, p ≥ 1, define the Lp norm of x by
Real numberIrrational numberComplex numberTranscendental number

Question 10: 1, the space of sequences whose series is ________,
IntegralHilbert spaceSeries (mathematics)Absolute convergence