It is known that if $K$ and $F$ are monotone, that $I+KF$ may not be monotone. For example, if $F(x,y)=(x+y, y-x) $ and $K(u,v)=(u+2v, v-2u)$ then $F$ and $K$ are monotone. However, $I+KF$ is not monotone. Question: What is the sufficient condition for the composotion of the two maps to be monotone? Or can the mapping $I+KF$ be written as the composition of some other mappings that are Monotone?
2026-03-26 19:00:53.1774551653
If $K$ and $F$ are monotone, when is $I+KF$ monotone?
28 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in OPERATOR-THEORY
- $\| (I-T)^{-1}|_{\ker(I-T)^\perp} \| \geq 1$ for all compact operator $T$ in an infinite dimensional Hilbert space
- Confusion about relationship between operator $K$-theory and topological $K$-theory
- Definition of matrix valued smooth function
- hyponormal operators
- a positive matrix of operators
- If $S=(S_1,S_2)$ hyponormal, why $S_1$ and $S_2$ are hyponormal?
- Closed kernel of a operator.
- Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?
- Show that a sequence of operators converges strongly to $I$ but not by norm.
- Is the dot product a symmetric or anti-symmetric operator?
Related Questions in FIXED-POINT-THEOREMS
- Newton's method with no real roots
- Determine $ \ a_{\max} \ $ and $ \ a_{\min} \ $ so that the above difference equation is well-defined.
- Show that $\Phi$ is a contraction with a maximum norm.
- Using Fixed point iteration to find sum of a Serias
- Map a closed function $f: (1,4) \rightarrow (1,4)$ without fixed point
- Stop criterium for fixed point methods
- Approximate solutions to nonlinear differential equations using an integral sequence
- Inverse function theorem via degree theory
- Fixed point of a map $\mathbb R^n \rightarrow \mathbb R^n$
- Why does the recursion $x_{n+1} = f(x_n)$ with $f(x) = p^k\cdot\sqrt[k+1]{x}$ converge to $p^{k+1}$?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- 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?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- 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
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?