University of Texas, Dolph Briscoe Center for American History

A Guide to the B. J. Pettis Papers, 1938-1980



Descriptive Summary

Creator: Pettis, B. J.
Title: B. J. Pettis Papers
Dates: 1938-1980
Abstract: Billy James (B. J.) Pettis (1913-1979) received his Ph.D. in 1937 from the University of Virginia. Pettis was first a Professor of Mathematics at Tulane University and then at the University of North Carolina at Chapel Hill from 1957 until his death in 1979. This collection primarily consists of annotated reprints, mathematical notes, lecture notes, and subject files.
Accession No.: 2005-204
Extent: 1 ft., 6 in.
Laguage: Materials are written in English.
Repository: Dolph Briscoe Center for American History, The University of Texas at Austin

Biographical Note

Billy James (B. J.) Pettis (1913-1979) received his Ph.D. in 1937 from the University of Virginia. Pettis was first a Professor of Mathematics at Tulane University and then at the University of North Carolina at Chapel Hill from 1957 until his death in 1979. Pettis produced fundamental work in functional analysis, including the general theory of Pettis Integration that is used in control theory and areas of pure mathematics. Pettis is also known for the Orlicz-Pettis Theorem, the Dunford-Pettis Theorem, and the Pettis Theorem on Measurability.


Scope and Contents

This collection primarily consists of annotated reprints, mathematical notes, lecture notes, and subject files.

Forms part of the Archives of American Mathematics.


Restrictions

Access Restrictions

Unrestricted access.


Index Terms

Pettis, Billy James
University of North Carolina at Chapel Hill. Dept. of Mathematics.

Administrative Information

Preferred Citation

B. J. Pettis Papers, 1938-1980, Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas at Austin.


Detailed Description of the Papers

 
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4RM139 General correspondence, 1975 and undated



 

Works by Pettis:

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4RM139 “Closed Graph and Open Mapping Theorem in Metrically Complete Spaces” [includes drafts and notes], undated
Duke talk, “Open Mapping and Closed Graph Theorems; or Ancient Monuments Revisited,” North Carolina Analysis Colloquium [includes draft copies and notes], 1971-1975 and undated
“On Some Theorems of Sierpinski on Subalgebras of Boolean σ-Rings” by B. J. Pettis [annotated reprint with separate notes], 1970 and undated
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4RM167 “S – G – P Seminar: 20 Jan 1977. Difference Theorems, and Gelfand’s 1935 Lemma and Some of Its Recent Successors” [photocopy of handwritten manuscript], 1977
“On the Radon-Nikodym Theorem” [typescript], undated
“Open Homomorphisms via Somewhere Denseness” [typescript], undated
“Some Topological Questions Related to Open Mapping and Closed Graph Theorems” in Studies in Topology, New York: Academic Press, Inc., 1975
Reprints:
“A Note on Regular Banach Spaces,” in Bulletin of the American Mathematical Society, June 1938
“Linear Functions and Completely Additive Set Functions,” in Duke Mathematical Journal, 4 (3), September, 1938
“On Integration in Vector Spaces,” in Transactions of the American Mathematical Society, 44 (2), September 1938
“Differentiation in Banach Spaces,” in Duke Mathematical Journal, 5 (2), June, 1939
“A Proof that Every Uniformly Convex Space is Reflexive” in Duke Mathematical Journal, 5 (2), June 1939
“Linear Operations Among Summable Functions,” in Proceedings from the National Academy of Sciences, 25 (10), October, 1939
“Linear Operations on Summable Functions,” Transactions of the American Mathematical Society, 47 (3), May, 1940
“On Continuity and Openness of Homomorphisms in Topological Groups,” in Annals of Mathematics, 52 (2), September 1950
“Remarks on a Theorem of E. J. McShane” in Proceedings of the American Mathematical Society, 2 (1), February, 1951
“On the Continuity of Parametric Linear Operations” in Proceedings of the American Mathematical Society, 2 (3), June, 1951
“On the Extension of Measures” in Annals of Mathematics, 54 (1), July, 1951
“Uniform Cauchy Points and Points of Equicontinuity” in American Journal of Mathematics, 73 (3), July, 1951
“Notes on Measure Theorey: Part 1. Lattices and Lattice Functionals,” Technical Report No. 2, Prepared under Contract N7-ONR-434 Task Order III for Office of Naval Research. Department of Mathematicas, Tulane University August 1, 1951
“A Note on Everywhere Dense Subgroups,” Proceedings of the American Mathematical Society, 3 (2), April, 1952
“Comments on Open Homomorphisms,” in Proceedings of the American Mathematical Society, 8 (3), June, 1957
“On a Vector Space Construction by Hausdorff,” in Proceedings of the American Mathematical Society, 8 (3), June, 1957
“A Comment on Compactness,” in American Mathematical Monthly, 75 (5), May, 1968
“Award for Distinguished Service to Professor Edward G. Begle,” in American Mathematical Monthly, 76 (1), January, 1969
“Cluster Sets of Nets,” in Proceedings of the American Mathematical Society, 22 (2), August, 1969
“On Nikaidô’s proof of the invariant mean-value theorem,” in Studia Mathematica, T. XXXIII, 1969
“On Some Theorems of Sierpinski on Subalgebras of Booleans [sigma]-Rings” in Bulletin de L’Academie Polonaise des Sciences, 19 (7), 1971
“Closed Graph and Open Mapping Theorems in Certain Topologically Complete Spaces,” in Bull. London Math. Soc., 6 [includes typescript with corrections and annotated preprint], 1974
“Addition to the Note: Closed Graph and Open Mapping Theorems in Certain Topologically Complete Spaces,” in Bull. London Math. Soc., 7, 1975



 

Works not by Pettis:

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4RM139 Reprints [with annotations by Pettis]:
“Théorie des sous – Mesures application a l’intégration vectorielle” by Jean-Claude Massé [includes correspondence], 1974-1975 and undated
American Mathematical Monthly 8(4), April 1973 [includes mathematical notes], 1951, 1973 and undated
“On Infinite-dimensional Linear Spaces” by G. W. Mackey, 1945
“Prolongement des Mesures Vectorielles” by Gr. Arsene and S. Stratila, 1965
“Applications of Almost Periodic Compactifications” by Karel Deleeuw and Irving Glicksburg, 1961 and undated
“Stefan Banach - exposé fait par M. H. Steinhaus le 4 septembre 1960 à Varsovie à l’occasion de la Conférence de l’Analyse Fonctionnelle,” 1960
“Generalized Means” by F. B. Wright in Transactions of the AMS, 98 (2), 187-203, 1961
Proceedings on the Symposium on Spectral Theory and Differential Problems, 1951 and undated
Assorted reprints [photocopies], 1957-1972



 

Lecture notes:

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4RM139 Carl Pearcy [“Some Recent Developments in Operator Theory”], undated
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4RM166 Rings of operators notes by Irving Kaplansky, 1955
Topological algebra notes by Irving Kaplansky, 1952 and undated
“The Revolution in Mathematics” by Marshall Stone, 1961
G. Whaples [includes algebraic number theory and class field theory lectures], 1964-1965 and undated



 

Subject files:

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4RM166 Closed graphs, etc., 1970-1973 and undated
Cluster sets, 1948, 1971 and undated
Continuity stuff [includes correspondence with H. E. White, Jr., a reprint of “On the Continuity of Parametric Linear Operations” by Pettis, and mathematical work], 1951-1972 and undated
Difference theorems, 1977-1978 and undated
Differentiation, 1968-1971 and undated
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4RM138 Generalized convexity, 1956-1973 and undated
Integration, 1973 and undated



 
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4RM167 Pettis memorial [includes biographical information], 1978-1979 and undated



 
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4RM167 Pettis conference [includes correspondence], 1979-1980 and undated



 
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4RM138 La Géométrie des Groupes Classiques by Jean Dieudonné [photocopy], 1963



 
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4RM138 [Unfoldered mathematical notes], 1967-1977 and undated



 
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4RM167 Index cards of bibliographic citations [some include annotations, approximately 3 inches], undated