Let $L^1_{\mu}$ be a separable $L^1$ space for a Borel measure $\mu$. Does there exists a (continuous) involution $i$ on $L^1_{\mu}$, such that $$ i(f \circ g) = g\circ f; $$ whenever composition is well-defined?
2025-01-13 05:41:51.1736746911
Involution of $L^1$ reversing composition order
42 Views Asked by ABIM https://math.techqa.club/user/abim/detail AtRelated Questions in FUNCTIONAL-ANALYSIS
- equivalent definitions of weak topology on a topological vector space
- Interpreting function notation?
- Dimension of $\ell^{1}$.
- Existence of an element in the infinite dimensional normed linear space?
- Confusing on lower semi continuous and its application in minimize problem
- Uniform and Compact Open Topology on spaces of maps from $\mathbb{R} \rightarrow \mathbb{R}$
- Trace Class: Relativeness
- Extension theorem for Sobolev spaces $W^{1,\infty}(\Omega)$: is there an elementary proof?
- Counterexample to $L^1$-boundedness of the maximal operator $f \mapsto f^\#$ with $f^{\sharp}(x):=\sup_{Q\ni x}\frac{1}{|Q|}\int_{Q}|f-(f)_{Q}|dy$
- Video lectures on Functional Analysis
Related Questions in INVOLUTIONS
- Normal unit vector
- Lineal functions problem; interpreting $\;{g}^{-1}(x)=g(x)$
- The conjugate of a complex function
- Involutions on semisimple Banach algebras are continuous
- What do we call the set of elements fixed by an involution of the second kind?
- On cardinality of involutions
- Involutions in $\mathbb{Q}$.
- On products of involutions
- $y=x/(1+a(x))$, $\quad$ $x=y/(1+b(y))$. What is known about $a\mapsto b$?
- Involution of $L^1$ reversing composition order
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity