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Topic · Mathematical Physics

Advanced Banach Space Theory

Advanced Banach Space Theory is a research topic within Mathematical Physics. Science Explorer counts 18k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in the theory of Banach spaces and operators, including functional analysis, topological vector spaces, holomorphic functions, summing operators, Bohr inequality, Lipschitz functions, geometric aspects, and approximation theory.

  • Banach Spaces
  • Operators
  • Functional Analysis
  • Topological Vector Spaces
  • Holomorphic Functions
  • Summing Operators
  • Bohr Inequality
  • Lipschitz Functions
  • Geometric Aspects
  • Approximation Theory
Research works
18k
fractional, since 1950
In the world top 10%
1.7k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+12%
the tick is no change
Largest producer
China
17% of the 10 largest, 2022-now
Advanced Banach Space Theory

Which countries lead Advanced Banach Space Theory research?

By volume, China and the United States publish the most (232 and 211 works in 2022-now).

By volume, 2022-now

  1. 1 China 232 works
  2. 2 United States 211 works
  3. 3 India 194 works
  4. 4 Russia 156 works
  5. 5 Spain 145 works
  6. 6 Poland 97 works
  7. 7 Türkiye 85 works
  8. 8 Iran 75 works
  9. 9 France 71 works
  10. 10 Germany 62 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 17.5%United States: 15.9%India: 14.6%Russia: 11.8%6 others listed: 40.2%17%largest
China232 · 17.5%United States211 · 15.9%India194 · 14.6%Russia156 · 11.8%6 others listed534 · 40.2%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Banach Space Theory research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Banach Space Theory research, followed by Russian Academy of Sciences and Lomonosov Moscow State University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 36 works
  2. 2 Russian Academy of SciencesRussia 36 works
  3. 3 Lomonosov Moscow State UniversityRussia 27 works
  4. 4 Universitat Politècnica de ValènciaSpain 21 works
  5. 5 Polish Academy of SciencesPoland 20 works
  6. 6 Universidad de GranadaSpain 15 works
  7. 7 Vasyl Stefanyk Carpathian National UniversityUkraine 13 works
  8. 8 Charles UniversityCzechia 12 works
  9. 9 Moscow Center For Continuous Mathematical EducationRussia 12 works
  10. 10 Czech Academy of SciencesCzechia 12 works

Who are the leading researchers in Advanced Banach Space Theory?

The most-cited researchers publishing on Advanced Banach Space Theory include R. W. L. Jones and John A. Todd.

  1. 1 R. W. L. Jones United Kingdom 189k citations
  2. 2 John A. Todd United Kingdom 107k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Advanced Banach Space Theory?

The most cited paper in Advanced Banach Space Theory is "Topological Vector Spaces." (M. S. Ramanujan, Helmut Schaefer, 1967), with 3,968 citations. Next come "Hp spaces of several variables" (2,887) and "Proximité et dualité dans un espace hilbertien" (1,450).

Most cited papers
#PaperReleasedCitations
1 Topological Vector Spaces. M. S. Ramanujan, Helmut Schaefer · American Mathematical Monthly Mar 1967 3,968
2 Hp spaces of several variables Charles Fefferman, E. M. Stein · Acta Mathematica 1972 2,887
3 Proximité et dualité dans un espace hilbertien Jean Jacques Moreau · Bulletin de la Société mathématique de France Open access 1965 1,450
4 Vector-valued laplace transforms and cauchy problems Wolfgang Arendt · Israel Journal of Mathematics Oct 1987 1,437
5 Inequalities in Banach spaces with applications Hong‐Kun Xu · Nonlinear Analysis 1991 1,095
All 100 most cited papers, with filters and sorting

Where is Advanced Banach Space Theory research done?

The largest centres of Advanced Banach Space Theory research in 2022-now are Moscow (Russia), Prague (Czechia), Warsaw (Poland) and Valencia (Spain).

Largest cities, 2022-now

  1. 1 MoscowRussia 66 works
  2. 2 PragueCzechia 34 works
  3. 3 WarsawPoland 29 works
  4. 4 ValenciaSpain 29 works
  5. 5 BeijingChina 29 works
  6. 6 MadridSpain 26 works
  7. 7 ViennaAustria 22 works
  8. 8 KolkataIndia 21 works
  9. 9 ParisFrance 20 works
  10. 10 TehranIran 20 works
See Advanced Banach Space Theory on the map

Where is the best place to study Advanced Banach Space Theory?

Among universities, judged by research, Moscow Center For Continuous Mathematical Education, Lomonosov Moscow State University and Vasyl Stefanyk Carpathian National University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 19.59%fractional works in this field (log) →share of work in the world top 10% →Vasyl Stefanyk Carpa…Moscow Center For Co…Lomonosov Moscow Sta…University of Sfax
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Moscow Center For Continuous Mathematical EducationRussia 75.330.6%375.8×12 +222.6%
2Lomonosov Moscow State UniversityRussia 72.619.2%16.0×27 +55.3%
3Vasyl Stefanyk Carpathian National UniversityUkraine 70.236.5%70.3×12 +16.6%
4University of SfaxTunisia 59.014.8%23.0×11 +37.9%
5Universitat Politècnica de ValènciaSpain 58.113.0%30.6×21 -1.0%
6University of ViennaAustria 57.323.2%9.8×10 +68.9%
7Jadavpur UniversityIndia 52.720.7%17.6×10 +159.3%
8Charles UniversityCzechia 50.210.9%13.5×12 +67.3%
9University of AlbertaCanada 49.615.8%6.4×11 +150.6%
10Universidad de GranadaSpain 49.311.2%13.2×15 +5.0%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Banach Space Theory, country by country

Is Advanced Banach Space Theory research growing?

Output in 2022-2025 was 12% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Advanced Banach Space Theory.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Banach Space Theory as a percentage of every work published that year, 0.0090% in 2024.

still counting0.025%0.050%0.075%Advanced Banach Space Theory0.0092% in 202519801990200020102020

Fractional works of Advanced Banach Space Theory over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Banach Space Theory9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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