In mathematics, **holomorphic functional calculus** is functional calculus with holomorphic functions. That is to say, given a holomorphic function *ƒ* of a complex argument *z* and an operator *T*, the aim is to construct an operator

which in a sense extends the function *ƒ* from complex argument to operator argument.

This article will discuss the case where *T* is a bounded linear operator on some Banach space. In particular, *T* can be a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights for the assumptions involved in the general construction.

Read more about Holomorphic Functional Calculus: Functional Calculus For A Bounded Operator, Spectral Considerations, Related Results

### Other articles related to "holomorphic functional calculus, holomorphic":

**Holomorphic Functional Calculus**

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**holomorphic functional calculus**... The

**holomorphic functional calculus**is defined as follows Fix a bounded operator T ... Consider the family Hol(T) of complex functions that is

**holomorphic**on some open set G containing σ(T) ...

**Holomorphic Functional Calculus**- Related Results - Unbounded Operators

... A

**holomorphic functional calculus**can be defined in a similar fashion for unbounded closed operators with non-empty resolvent set ...

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