Descriptive Summary
Pettis, B. J.
B. J. Pettis
Papers
1938-1980Materials are
written in English.
2005-204
1 ft., 6 in.
Dolph Briscoe Center for American
History, The University of Texas at
Austin
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.
Biographical NoteBilly 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 ContentsThis collection primarily consists of
annotated reprints, mathematical notes, lecture notes, and subject
files.

Forms part of the Archives of American Mathematics.

Access RestrictionsUnrestricted access.

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

Index Terms
Pettis, Billy James
University of North Carolina at Chapel
Hill. Dept. of Mathematics.
Detailed Description of the Papers
4RM139
General correspondence,
1975 and undated
Works by Pettis:
4RM139
“Closed Graph and Open Mapping Theorem in Metrically
Complete Spaces” [includes drafts and notes],
undated
4RM139
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
4RM139
“On Some Theorems of Sierpinski on Subalgebras of Boolean
σ-Rings” by B. J. Pettis [annotated reprint with separate notes],
1970 and undated
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
4RM167
“On the Radon-Nikodym Theorem” [typescript],
undated
4RM167
“Open Homomorphisms via Somewhere Denseness” [typescript],
undated
4RM167
“Some Topological Questions Related to Open Mapping and
Closed Graph Theorems” in
Studies in Topology, New York:
Academic Press, Inc.,
1975
4RM167
Reprints:
4RM167
“A Note on Regular Banach Spaces,” in
Bulletin of the American Mathematical
Society,
June 1938
4RM167
“Linear Functions and Completely Additive Set
Functions,” in
Duke Mathematical Journal, 4 (3),
September, 1938
4RM167
“On Integration in Vector Spaces,” in
Transactions of the American Mathematical
Society, 44 (2),
September 1938
4RM167
“Differentiation in Banach Spaces,” in
Duke Mathematical Journal, 5 (2),
June, 1939
4RM167
“A Proof that Every Uniformly Convex Space is Reflexive”
in
Duke Mathematical Journal, 5 (2),
June 1939
4RM167
“Linear Operations Among Summable Functions,” in
Proceedings from the National Academy of
Sciences, 25 (10),
October, 1939
4RM167
“Linear Operations on Summable Functions,”
Transactions of the American Mathematical
Society, 47 (3),
May, 1940
4RM167
“On Continuity and Openness of Homomorphisms in
Topological Groups,” in
Annals of Mathematics, 52 (2),
September 1950
4RM167
“Remarks on a Theorem of E. J. McShane” in
Proceedings of the American Mathematical
Society, 2 (1),
February, 1951
4RM167
“On the Continuity of Parametric Linear Operations” in
Proceedings of the American Mathematical
Society, 2 (3),
June, 1951
4RM167
“On the Extension of Measures” in
Annals of Mathematics, 54 (1),
July, 1951
4RM167
“Uniform Cauchy Points and Points of Equicontinuity” in
American Journal of Mathematics,
73 (3),
July, 1951
4RM167
“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
4RM167
“A Note on Everywhere Dense Subgroups,”
Proceedings of the American Mathematical
Society, 3 (2),
April, 1952
4RM167
“Comments on Open Homomorphisms,” in
Proceedings of the American Mathematical
Society, 8 (3),
June, 1957
4RM167
“On a Vector Space Construction by Hausdorff,” in
Proceedings of the American Mathematical
Society, 8 (3),
June, 1957
4RM167
“A Comment on Compactness,” in
American Mathematical Monthly, 75
(5),
May, 1968
4RM167
“Award for Distinguished Service to Professor Edward G.
Begle,” in
American Mathematical Monthly, 76
(1),
January, 1969
4RM167
“Cluster Sets of Nets,” in Proceedings of the
American Mathematical Society, 22
(2),
August, 1969
4RM167
“On Nikaidô’s proof of the invariant mean-value
theorem,” in
Studia Mathematica, T. XXXIII,
1969
4RM167
“On Some Theorems of Sierpinski on Subalgebras of
Booleans [sigma]-Rings” in
Bulletin de L’Academie Polonaise des
Sciences, 19 (7),
1971
4RM167
“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
4RM167
“Addition to the Note: Closed Graph and Open Mapping
Theorems in Certain Topologically Complete Spaces,” in
Bull. London Math. Soc., 7,
1975
4RM167
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Works not by Pettis:
4RM139
Reprints [with annotations by Pettis]:
4RM139
“Théorie des sous – Mesures application a l’intégration
vectorielle” by Jean-Claude Massé [includes correspondence],
1974-1975 and undated
4RM139
American Mathematical Monthly
8(4), April 1973 [includes mathematical notes],
1951, 1973 and undated
4RM139
“On Infinite-dimensional Linear Spaces” by G. W. Mackey,
1945
4RM139
“Prolongement des Mesures Vectorielles” by Gr. Arsene
and S. Stratila,
1965
4RM139
“Applications of Almost Periodic Compactifications” by
Karel Deleeuw and Irving Glicksburg,
1961 and undated
4RM139
“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
4RM139
“Generalized Means” by F. B. Wright in
Transactions of the AMS, 98 (2),
187-203,
1961
4RM139
Proceedings on the Symposium on Spectral
Theory and Differential Problems,
1951 and undated
4RM139
Assorted reprints [photocopies],
1957-1972
Lecture notes:
4RM139
Carl Pearcy [“Some Recent Developments in Operator
Theory”],
undated
4RM166
Rings of operators notes by Irving Kaplansky,
1955
4RM166
Topological algebra notes by Irving Kaplansky,
1952 and undated
4RM166
“The Revolution in Mathematics” by Marshall Stone,
1961
4RM166
G. Whaples [includes algebraic number theory and class
field theory lectures],
1964-1965 and undated
Subject files:
4RM166
Closed graphs, etc.,
1970-1973 and undated
4RM166
Cluster sets,
1948, 1971 and undated
4RM166
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
4RM166
Difference theorems,
1977-1978 and undated
4RM166
Differentiation,
1968-1971 and undated
4RM138
Generalized convexity,
1956-1973 and undated
4RM138
Integration,
1973 and undated
4RM167
Pettis memorial [includes biographical information],
1978-1979 and undated
4RM167
Pettis conference [includes correspondence],
1979-1980 and undated
4RM138
La Géométrie des Groupes Classiques by
Jean Dieudonné [photocopy],
1963
4RM138
[Unfoldered mathematical notes],
1967-1977 and undated
4RM167
Index cards of bibliographic citations [some include
annotations, approximately 3 inches],
undated