Notation. half arrow upwards

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In summary, the conversation discusses a notation involving a mapping and a set, with an arrow pointing upwards and a missing left hook. The context is operators in a Banach space, with the ascent of the operator defined as the minimum power where the kernel of that power is equal to the kernel of the next power. The notation T\upharpoonright T^p(X) is used to represent a mapping that is invertible.
  • #1
jostpuur
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I encountered notation that I don't know. It's like T|A where T is a mapping, and A is a set (little like a restriction), but the | is an arrow pointing upwards and the left hook is missing like with an arrow of a weak convergence.

Anyone knowing what that means? Or a keyword that I could put in google (I cannot put that half arrow there)
 
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What is the context?
 
  • #3
Operators. T:X->X is a continuous linear mapping in a Banach space, and an ascent of the operator is defined

[tex]
\textrm{ascent}(T) := \textrm{min}\;\{p\in\mathbb{N}\;|\; \textrm{ker}(T^p)=\textrm{ker}(T^{p+1})\}
[/tex]

The p is then assumed to be the ascent, and the notation

[tex]
T\upharpoonright T^p(X)
[/tex]

is used. This notation means some kind of mapping, because it is said to be invertible.
 

What does "half arrow upwards" notation mean?

"Half arrow upwards" notation is a mathematical symbol used to indicate that a value or variable is approaching a certain limit or infinity. It is often used in calculus and other branches of mathematics.

How is "half arrow upwards" notation written?

The "half arrow upwards" symbol is represented by the symbol → placed above the value or variable it is referencing. For example, if we want to indicate that a variable x is approaching infinity, we would write x → ∞.

What is the difference between "half arrow upwards" notation and "half arrow downwards" notation?

The difference between these two notations lies in the direction of the arrow. "Half arrow upwards" (→) indicates that the value or variable is approaching a limit or infinity from below, while "half arrow downwards" (←) indicates the opposite, that the value or variable is approaching a limit or infinity from above.

How do I know when to use "half arrow upwards" notation?

"Half arrow upwards" notation is typically used in mathematical expressions or equations where we want to indicate the behavior of a value or variable as it approaches a certain limit or infinity. It is commonly used in calculus, but can also be seen in other areas of mathematics.

What is the purpose of "half arrow upwards" notation?

The purpose of "half arrow upwards" notation is to provide a concise and standardized way of representing the behavior of a value or variable as it approaches a limit or infinity. It allows for a more precise and efficient communication of mathematical ideas and concepts.

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