A Guide to the B. J. Pettis Papers, 19381980





Creator: 
Pettis, B. J. 

Title: 
B. J. Pettis
Papers 

Dates: 
19381980 

Abstract: 
Billy James (B. J.)
Pettis (19131979) 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.: 
2005204 

Extent: 
1 ft., 6 in. 

Laguage: 
Materials are
written in English. 

Repository: 
Dolph Briscoe Center for American
History, The University of Texas at
Austin 
Billy James (B. J.) Pettis (19131979)
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 OrliczPettis Theorem, the
DunfordPettis Theorem, and the Pettis Theorem on Measurability.
This collection primarily consists of
annotated reprints, mathematical notes, lecture notes, and subject
files.
Forms part of the Archives of American Mathematics.
Access Restrictions
Unrestricted access.










Pettis, Billy James 


University of North Carolina at Chapel
Hill. Dept. of Mathematics. 
B. J. Pettis Papers, 19381980, Archives
of American Mathematics, Dolph Briscoe Center for American History, University of
Texas at Austin.
Detailed Description of the Papers















box 
4RM139 

General correspondence,
1975 and undated 















Works by Pettis: 
box 
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],
19711975 and undated 



“On Some Theorems of Sierpinski on Subalgebras of Boolean
σRings” by B. J. Pettis [annotated reprint with separate notes],
1970 and undated 
box 
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 RadonNikodym 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 N7ONR434 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 meanvalue
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: 
box 
4RM139 


Reprints [with annotations by Pettis]: 




“Théorie des sous – Mesures application a l’intégration
vectorielle” by JeanClaude Massé [includes correspondence],
19741975 and undated 




American Mathematical Monthly
8(4), April 1973 [includes mathematical notes],
1951, 1973 and undated 




“On Infinitedimensional 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),
187203,
1961 




Proceedings on the Symposium on Spectral
Theory and Differential Problems,
1951 and undated 




Assorted reprints [photocopies],
19571972 















Lecture notes: 
box 
4RM139 


Carl Pearcy [“Some Recent Developments in Operator
Theory”],
undated 
box 
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],
19641965 and undated 















Subject files: 
box 
4RM166 


Closed graphs, etc.,
19701973 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],
19511972 and undated 



Difference theorems,
19771978 and undated 



Differentiation,
19681971 and undated 
box 
4RM138 


Generalized convexity,
19561973 and undated 



Integration,
1973 and undated 















box 
4RM167 

Pettis memorial [includes biographical information],
19781979 and undated 















box 
4RM167 

Pettis conference [includes correspondence],
19791980 and undated 















box 
4RM138 

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















box 
4RM138 

[Unfoldered mathematical notes],
19671977 and undated 















box 
4RM167 

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