He means the left and right side of the equation. Your equation is not how the operator norm is defined so this is the first thing you need to find out.Frobenius21 said:Im sorry, I missed the square root.
What do you mean by the thing on the left/right? Do you mean the left hand side and the right hand side of the equation?
Or do you mean the left and right terms in the integral?
The norm of an operator Tf(t) is a measure of the size or magnitude of the operator. It is calculated by taking the supremum (least upper bound) of the operator's image under all possible inputs. In other words, it is the maximum amount by which the operator can magnify an input.
The norm of an operator Tf(t) is a measure of the operator's size or magnitude, while the norm of a vector is a measure of the vector's length. While the norm of a vector is a single number, the norm of an operator is a function that maps inputs to outputs.
The norm of an operator Tf(t) is an important concept in functional analysis and linear algebra. It is used to study the properties of operators and their behavior under various operations, such as composition and inversion. The norm also plays a crucial role in defining convergence and continuity of operators.
The norm of an operator Tf(t) is typically calculated using the operator norm formula, which involves taking the supremum of the operator's image under all possible inputs. In some cases, the norm can also be calculated using other methods, such as the spectral norm or the Frobenius norm.
No, the norm of an operator Tf(t) cannot be negative. By definition, the norm is always a non-negative number. It represents the magnitude of the operator and cannot have a negative value. If the norm of an operator is zero, it means that the operator is a zero operator, meaning it maps all inputs to the zero vector.