**Errett Bishop** was an American mathematician who worked in analysis.

- Errett did not find High School at all challenging and when he was sixteen, wanting to progress with his education in a way that was not happening at school, he applied and was accepted for a special scholarship program at the University of Chicago.
- Starting his university studies in 1944, Bishop graduated with a B.S. from Chicago in 1947 and continued to study for his Master's degree which was awarded in 1947.
- Bishop had been taught by Paul Halmos when he was studying for his B.S. and it was Halmos who supervised his doctoral studies.
- However Bishop spent 1950-52 in the U.S. army.
- After completing his basic army training Bishop was sent to undertake mathematical research at the National Bureau of Standards.
- Returning to Chicago in 1952 Bishop submitted his doctoral thesis Spectral Theory for Operations on Banach Spaces in 1954.
- Having submitted his thesis, Bishop was appointed as an instructor in mathematics at the University of California at Berkeley.
- Bishop's work is so wide ranging that it is difficult to give an overview in a biography such as this.
- Let us look at the book Selected papers which was published in 1986 and reprints some of Bishop's most significant contributions.
- Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures.
- In 1965 Bishop wrote an excellent survey Uniform algebras examining the interaction between the theory of uniform algebras and that of several complex variables.
- An examples of a paper by Bishop on this topic is Spectral theory for operators on a Banach space (1957).
- He introduced the condition now called the Bishop condition which turned out to be very useful in the theory of decomposable operators.
- Examples of Bishop's papers in this area are Analyticity in certain Banach spaces (1962).
- Bishop become interested in foundational issues around 1964, about the time he was at the Miller Institute.
- Many other areas of mathematics were given the constructive treatment by Bishop.
- In the following year Bishop published Schizophrenia in contemporary mathematics which gave his principles of constructivism.

Born 24 July 1928, Newton, Kansas, USA. Died 14 April 1983, San Diego, California, USA.

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Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive