That follows from the triangle inequality: $\|K\| = \|K-L+L\| \leqslant \|K-L\| + \|L\|.$sarrah said:Can I always say without reservation that for any two integral operators $K$ and $L$ defined as follows say
$(Ky)(x)=\int_{a}^{b} \,k(x,s)y(s)ds$
that
$||L||+||K-L||\ge||K||$
thanks
Sarrah
The norm of sum refers to the mathematical operation of finding the norm (or magnitude) of the sum of two or more vectors. It is commonly used in linear algebra and is denoted as ||x + y||, where x and y are vectors.
The norm of sum is calculated by first finding the sum of the individual vectors, then finding the norm of the resulting vector using a norm function such as the Euclidean norm or the Manhattan norm.
The sum of norms is the mathematical operation of finding the sum of the norms (or magnitudes) of two or more vectors. It is also commonly used in linear algebra and is denoted as ||x|| + ||y||, where x and y are vectors.
The sum of norms is calculated by first finding the individual norms of each vector, then adding them together using basic arithmetic operations.
The concept of norm of sum and sum of norms is important in various branches of mathematics, including linear algebra, functional analysis, and geometry. It is used to measure the magnitude or size of vectors and is also used in various mathematical proofs and calculations.