--- a/test/LazyTensors/lazy_tensor_operations_test.jl	Wed Mar 16 18:32:59 2022 +0100
+++ b/test/LazyTensors/lazy_tensor_operations_test.jl	Wed Mar 16 18:39:00 2022 +0100
@@ -36,10 +36,8 @@
 
     m = SizeDoublingMapping{Int, 1, 1}((3,))
     v = [0,1,2]
-    @test m*v isa AbstractVector{Int}
     @test size(m*v) == 2 .*size(v)
     @test (m*v)[0] == (:apply,v,(0,))
-    @test m*m*v isa AbstractVector{Int}
     @test (m*m*v)[1] == (:apply,m*v,(1,))
     @test (m*m*v)[3] == (:apply,m*v,(3,))
     @test (m*m*v)[6] == (:apply,m*v,(6,))
@@ -80,6 +78,43 @@
     v = [[1 2];[3 4]]
     @test m*v == [[2 4];[6 8]]
     @test (m*v)[2,1] == 6
+
+    @testset "Type calculation" begin
+        m = ScalingOperator{Int,1}(2,(3,))
+        v = [1.,2.,3.]
+        @test m*v isa AbstractVector{Float64}
+        @test m*v == [2.,4.,6.]
+        @inferred m*v
+        @inferred (m*v)[1]
+
+        m = ScalingOperator{Int,2}(2,(2,2))
+        v = [[1. 2.];[3. 4.]]
+        @test m*v == [[2. 4.];[6. 8.]]
+        @test (m*v)[2,1] == 6.
+        @inferred m*v
+        @inferred (m*v)[1]
+
+        m = ScalingOperator{ComplexF64,1}(2. +2. *im,(3,))
+        v = [1.,2.,3.]
+        @test m*v isa AbstractVector{ComplexF64}
+        @test m*v == [2. + 2. *im, 4. + 4. *im, 6. + 6. *im]
+        @inferred m*v
+        @inferred (m*v)[1]
+
+        m = ScalingOperator{ComplexF64,1}(1,(3,))
+        v = [2. + 2. *im, 4. + 4. *im, 6. + 6. *im]
+        @test m*v isa AbstractVector{ComplexF64}
+        @test m*v == [2. + 2. *im, 4. + 4. *im, 6. + 6. *im]
+        @inferred m*v
+        @inferred (m*v)[1]
+
+        m = ScalingOperator{Float64,1}(2., (3,))
+        v = [[1,2,3], [3,2,1],[1,3,1]]
+        @test m*v isa AbstractVector{Vector{Float64}}
+        @test m*v == [[2.,4.,6.], [6.,4.,2.],[2.,6.,2.]]
+        @inferred m*v
+        @inferred (m*v)[1]
+    end
 end
 
 @testset "TensorMapping binary operations" begin
@@ -107,6 +142,8 @@
 
     @test range_size(A+B) == range_size(A) == range_size(B)
     @test domain_size(A+B) == domain_size(A) == domain_size(B)
+
+    @test ((A+B)*ComplexF64[1.1,1.2,1.3])[3] isa ComplexF64
 end
 
 
@@ -129,6 +166,9 @@
 
     v = rand(2)
     @test (Ã∘B̃)'*v ≈ B'*A'*v rtol=1e-14
+
+    @test (Ã∘B̃*ComplexF64[1.,2.,3.,4.])[1] isa ComplexF64
+    @test ((Ã∘B̃)'*ComplexF64[1.,2.])[1] isa ComplexF64
 end
 
 @testset "LazyLinearMap" begin
@@ -194,6 +234,10 @@
         @test I*v == v
         @test I'*v == v
 
+        v = rand(ComplexF64,sz...)
+        @test I*v == v
+        @test I'*v == v
+
         @test range_size(I) == sz
         @test domain_size(I) == sz
     end
@@ -322,6 +366,16 @@
             end
         end
 
+        @testset "application to other type" begin
+            tm = InflatedTensorMapping(I(3,2), A, I(4))
+
+            v = rand(ComplexF64, domain_size(tm)...)
+            @test (tm*v)[1,2,3,1] isa ComplexF64
+
+            v = rand(ComplexF64, domain_size(tm')...)
+            @test (tm'*v)[1,2,2,1] isa ComplexF64
+        end
+
         @testset "Inference of application" begin
             struct ScalingOperator{T,D} <: TensorMapping{T,D,D}
                 λ::T