diff --git a/Project.toml b/Project.toml
index d5f94a7..d8cf8f5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "FusionTensors"
 uuid = "e16ca583-1f51-4df0-8e12-57d32947d33e"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.5.1"
+version = "0.5.2"
 
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
diff --git a/src/fusiontensor/base_interface.jl b/src/fusiontensor/base_interface.jl
index 4def6f8..ea3241d 100644
--- a/src/fusiontensor/base_interface.jl
+++ b/src/fusiontensor/base_interface.jl
@@ -73,14 +73,19 @@ function Base.getindex(ft::FusionTensor, f1::SectorFusionTree, f2::SectorFusionT
   return reshape(charge_matrix, charge_block_size(ft, f1, f2))
 end
 
+Base.imag(ft::FusionTensor) = set_data_matrix(ft, imag(data_matrix(ft)))
+
+Base.permutedims(ft::FusionTensor, args...) = fusiontensor_permutedims(ft, args...)
+
+Base.real(ft::FusionTensor{<:Real}) = ft   # same object
+Base.real(ft::FusionTensor) = set_data_matrix(ft, real(data_matrix(ft)))
+
 function Base.setindex!(
   ft::FusionTensor, a::AbstractArray, f1::SectorFusionTree, f2::SectorFusionTree
 )
   return view(ft, f1, f2) .= a
 end
 
-Base.permutedims(ft::FusionTensor, args...) = fusiontensor_permutedims(ft, args...)
-
 function Base.similar(ft::FusionTensor, T::Type)
   # reuse trees_block_mapping
 
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 295cfc0..a575664 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -28,7 +28,7 @@ using GradedArrays:
   space_isequal
 using TensorAlgebra: tuplemortar
 using TensorProducts: tensor_product
-using LinearAlgebra: LinearAlgebra
+using LinearAlgebra: LinearAlgebra, norm
 using Random: Random
 
 include("setup.jl")
@@ -184,12 +184,53 @@ end
   @test sector_type(ft3) === TrivialSector
 end
 
+@testset "specific constructors" begin
+  g1 = gradedrange([U1(0) => 1, U1(1) => 2, U1(2) => 3])
+  g2 = gradedrange([U1(0) => 2, U1(1) => 2, U1(3) => 1])
+  g3 = gradedrange([U1(-1) => 1, U1(0) => 2, U1(1) => 1])
+  g4 = gradedrange([U1(-1) => 1, U1(0) => 1, U1(1) => 1])
+
+  fta = FusionTensorAxes((g1,), (g2, g3))
+  @test zeros(fta) isa FusionTensor{Float64,3}
+  @test zeros(ComplexF64, fta) isa FusionTensor{ComplexF64,3}
+
+  rng = Random.default_rng()
+  ft1 = randn(rng, ComplexF64, fta)
+  @test ft1 isa FusionTensor{ComplexF64,3}
+  @test all(!=(0), data_matrix(ft1)[Block(1, 5)])
+  @test randn(rng, fta) isa FusionTensor{Float64,3}
+  @test randn(ComplexF64, fta) isa FusionTensor{ComplexF64,3}
+  @test randn(fta) isa FusionTensor{Float64,3}
+
+  ft2 = FusionTensor(LinearAlgebra.I, (g1, g2))
+  @test ft2 isa FusionTensor{Float64,4}
+  @test axes(ft2) == FusionTensorAxes((g1, g2), dual.((g1, g2)))
+  @test collect(eachblockstoredindex(data_matrix(ft2))) == map(i -> Block(i, i), 1:6)
+  for i in 1:6
+    m = data_matrix(ft2)[Block(i, i)]
+    @test m == LinearAlgebra.I(size(m, 1))
+  end
+
+  ft2 = FusionTensor(3 * LinearAlgebra.I, (g1, g2))
+  @test ft2 isa FusionTensor{Float64,4}
+  @test axes(ft2) == FusionTensorAxes((g1, g2), dual.((g1, g2)))
+  @test collect(eachblockstoredindex(data_matrix(ft2))) == map(i -> Block(i, i), 1:6)
+  for i in 1:6
+    m = data_matrix(ft2)[Block(i, i)]
+    @test m == 3 * LinearAlgebra.I(size(m, 1))
+  end
+
+  @test FusionTensor{ComplexF64}(LinearAlgebra.I, (g1, g2)) isa FusionTensor{ComplexF64,4}
+end
+
 @testset "Base operations" begin
   g1 = gradedrange([U1(0) => 1, U1(1) => 2, U1(2) => 3])
   g2 = gradedrange([U1(0) => 2, U1(1) => 2, U1(3) => 1])
   g3 = gradedrange([U1(-1) => 1, U1(0) => 2, U1(1) => 1])
   g4 = gradedrange([U1(-1) => 1, U1(0) => 1, U1(1) => 1])
-  ft3 = FusionTensor{Float64}(undef, (g1, g2), (g3, g4))
+  ft3 = randn(FusionTensorAxes((g1, g2), (g3, g4)))
+  @test ft3 isa FusionTensor{Float64,4}
+  @test norm(ft3) ≉ 0
   @test isnothing(check_sanity(ft3))
 
   ft4 = +ft3
@@ -199,6 +240,8 @@ end
   @test isnothing(check_sanity(ft4))
   @test codomain_axes(ft4) === codomain_axes(ft3)
   @test domain_axes(ft4) === domain_axes(ft3)
+  @test norm(ft4) ≈ norm(ft3)
+  @test norm(ft4 + ft3) ≈ 0.0
 
   ft4 = ft3 + ft3
   @test codomain_axes(ft4) === codomain_axes(ft3)
@@ -206,6 +249,7 @@ end
   @test space_isequal(codomain_axis(ft4), codomain_axis(ft3))
   @test space_isequal(domain_axis(ft4), domain_axis(ft3))
   @test isnothing(check_sanity(ft4))
+  @test norm(ft4) ≈ 2norm(ft3)
 
   ft4 = ft3 - ft3
   @test codomain_axes(ft4) === codomain_axes(ft3)
@@ -213,6 +257,7 @@ end
   @test space_isequal(codomain_axis(ft4), codomain_axis(ft3))
   @test space_isequal(domain_axis(ft4), domain_axis(ft3))
   @test isnothing(check_sanity(ft4))
+  @test norm(ft4) ≈ 0.0
 
   ft4 = 2 * ft3
   @test codomain_axes(ft4) === codomain_axes(ft3)
@@ -221,6 +266,7 @@ end
   @test space_isequal(domain_axis(ft4), domain_axis(ft3))
   @test isnothing(check_sanity(ft4))
   @test eltype(ft4) == Float64
+  @test norm(ft4) ≈ 2norm(ft3)
 
   ft4 = 2.0 * ft3
   @test codomain_axes(ft4) === codomain_axes(ft3)
@@ -237,17 +283,27 @@ end
   @test space_isequal(domain_axis(ft4), domain_axis(ft3))
   @test isnothing(check_sanity(ft4))
   @test eltype(ft4) == Float64
+  @test norm(ft4) ≈ norm(ft3) / 2.0
 
-  ft5 = 2.0im * ft3
+  ft5 = (1.0 + 2.0im) * ft3
   @test codomain_axes(ft5) === codomain_axes(ft3)
   @test domain_axes(ft5) === domain_axes(ft3)
   @test space_isequal(codomain_axis(ft5), codomain_axis(ft3))
   @test space_isequal(domain_axis(ft5), domain_axis(ft3))
   @test isnothing(check_sanity(ft4))
   @test eltype(ft5) == ComplexF64
+  @test norm(ft5) ≈ √5 * norm(ft3)
 
-  ft4 = conj(ft3)
-  @test ft4 === ft3  # same object
+  @test conj(ft3) === ft3  # same object
+  @test real(ft3) === ft3
+  @test norm(imag(ft3)) == 0
+
+  @test conj(ft5) isa FusionTensor{ComplexF64,4}
+  @test real(ft5) isa FusionTensor{Float64,4}
+  @test imag(ft3) isa FusionTensor{Float64,4}
+  @test conj(ft5) ≈ (1.0 - 2.0im) * ft3
+  @test real(ft5) ≈ ft3
+  @test imag(ft5) ≈ 2ft3
 
   ft6 = conj(ft5)
   @test ft6 !== ft5  # different object
@@ -257,6 +313,7 @@ end
   @test space_isequal(codomain_axis(ft6), codomain_axis(ft5))
   @test space_isequal(domain_axis(ft6), domain_axis(ft5))
   @test eltype(ft6) == ComplexF64
+  @test ft6 + ft5 ≈ 2 * real(ft5)
 
   ad = adjoint(ft3)
   @test ad isa FusionTensor
@@ -274,45 +331,6 @@ end
   @test_throws ArgumentError ft7 * ft3
 end
 
-@testset "specific constructors" begin
-  g1 = gradedrange([U1(0) => 1, U1(1) => 2, U1(2) => 3])
-  g2 = gradedrange([U1(0) => 2, U1(1) => 2, U1(3) => 1])
-  g3 = gradedrange([U1(-1) => 1, U1(0) => 2, U1(1) => 1])
-  g4 = gradedrange([U1(-1) => 1, U1(0) => 1, U1(1) => 1])
-
-  fta = FusionTensorAxes((g1,), (g2, g3))
-  @test zeros(fta) isa FusionTensor{Float64,3}
-  @test zeros(ComplexF64, fta) isa FusionTensor{ComplexF64,3}
-
-  rng = Random.default_rng()
-  ft1 = randn(rng, ComplexF64, fta)
-  @test ft1 isa FusionTensor{ComplexF64,3}
-  @test all(!=(0), data_matrix(ft1)[Block(1, 5)])
-  @test randn(rng, fta) isa FusionTensor{Float64,3}
-  @test randn(ComplexF64, fta) isa FusionTensor{ComplexF64,3}
-  @test randn(fta) isa FusionTensor{Float64,3}
-
-  ft2 = FusionTensor(LinearAlgebra.I, (g1, g2))
-  @test ft2 isa FusionTensor{Float64,4}
-  @test axes(ft2) == FusionTensorAxes((g1, g2), dual.((g1, g2)))
-  @test collect(eachblockstoredindex(data_matrix(ft2))) == map(i -> Block(i, i), 1:6)
-  for i in 1:6
-    m = data_matrix(ft2)[Block(i, i)]
-    @test m == LinearAlgebra.I(size(m, 1))
-  end
-
-  ft2 = FusionTensor(3 * LinearAlgebra.I, (g1, g2))
-  @test ft2 isa FusionTensor{Float64,4}
-  @test axes(ft2) == FusionTensorAxes((g1, g2), dual.((g1, g2)))
-  @test collect(eachblockstoredindex(data_matrix(ft2))) == map(i -> Block(i, i), 1:6)
-  for i in 1:6
-    m = data_matrix(ft2)[Block(i, i)]
-    @test m == 3 * LinearAlgebra.I(size(m, 1))
-  end
-
-  @test FusionTensor{ComplexF64}(LinearAlgebra.I, (g1, g2)) isa FusionTensor{ComplexF64,4}
-end
-
 @testset "missing SectorProduct" begin
   g1 = gradedrange([SectorProduct(U1(1)) => 1])
   g2 = gradedrange([SectorProduct(U1(1), SU2(1//2)) => 1])